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LOGIC. 



BY 



W. STANLEY JEVONS, M.A., LL.D., F.R.S., 

PROFESSOR OF POLITICAL FXONOMY IN UNIVERSITY COLLEGE, LONDON. 



WITH ILLUSTRATIONS. 






NEW YORK •:• CINCINNATI •:• CHICAGO: 
AMERICAN BOOK COMPANY. 






PRIMER SERIES. 

SCIENCE PRIMERS. 

HUXLEY'S INTRODUCTORY VOLUME. 

ROSCOE'S CHEMISTRY. 

STEWART'S PHYSICS. 

GEIKIE'S GEOLOGY. 

LOCKYER'S ASTRONOMY. 

HOOKER'S BOTANY. 

FOSTER AND TRACY'S PHYSIOLOGY AND 

HYGIENE. 
GEIKIE'S PHYSICAL GEOGRAPHY. 
LUPTON'S SCIENTIFIC AGRICULTURE. 
JEVONS'S LOGIC. 

SPENCER'S INVENTIONAL GEOMETRY. 
JEVONS'S POLITICAL ECONOMY. 
TAYLOR'S PIANOFORTE PLAYING. 
PATTON'S NATURAL RESOURCES OF THE 

UNITED STATES. 

HISTORY PRIMERS. 

WENDEL'S HISTORY OF EGYPT. 
FREEMAN'S HISTORY OF EUROPE. 
FYFFE'S HISTORY OF GREECE. 
CREIGHTON'S HISTORY OF ROME. 
MAHAFFY'S OLD GREEK LIFE. 
WILKINS'S ROMAN ANTIQUITIES. 
TIGHE'S ROMAN CONSTITUTION. 
ADAMS S MEDIAEVAL CIVILIZATION. 
YONGE'S HISTORY OF FRANCE. 
GROVE'S GEOGRAPHY. 

LITERATURE PRIMERS. 

BROOKE'S ENGLISH LITERATURE. 

WATKINS'S AMERICAN LITERATURE. 

DOWDEN S SHAKSPERE. . < , , , 

ALD'EN'S STUDIES IN BRYANT. 
'MOttRIS'Jn ENGLISH GRAMMAR; 

MORRiS AND BOWEN'S ENGLISH 
GRAMMAR EXERCISES. 

NICHOTVS, ENGLISH COMPOSITION 
■ REILE'S PKI1.OLOGY. ', 
EBB'S' G^H:EK ".irERATURE. ; 

(GLADSTONES KOMFR. 

TOZER'S CLASSICAL GEOGRAPHY. 



jm 



JEVONS— LOGIC. 
W. P 9 



LC Control Number 




tmp96 026013 



CONTENTS. 



SECT. --AGE 

I. — Introduction 7 

II. — How WE Commonly Reason ..... 9 

III. — What IS Deductive Reasoning ? ... 12 

IV. — The Different Kinds of Terms or 

Names 15 

V. — The Full Meaning of Terms ..... 20 

VI. — The Correct Use of Words 22 

VII. — How and Why we Classify Things . . 27 

VIII. — Propositions 37 

IX. — How TO Change Propositions .... 47 

X. — The Syllogism 53 

XL — The Rules of the Syllogism . » . . 56 

XII. — Hypothetical Syllogisms 69 

XIII. — Other Kinds of Arguments . . , 71 

XIV. — The Great Rule of Inference .... 73 

XV. — Inductive Reasoning 76 

XVI. — Inductive Reasoning in Ordinary Life . 85 

XVIL— Observation and Experiment .... 89 



CONTENTS, 



SECT. PAGE 

XVIII. — Antecedents and Causes of Events . . 92 

XIX. — Discovery of Agreements 95 

XX. — Things which Vary in Quantity ... 97 

XXI.— Things which Vary Periodically ... 99 

XXII. —Reasoning from Experiments .... 102 

XXIII. — How AND When to Generalize . . . . 104 

XXIV. — Reasoning by Analogy . 107 

XXV.— Fallacies , o 112 

XXVI. — Fallacies of Ambiguity ...... 114 

XXVII. — Fallacies in Inductive Reasoning . . 12a 



SCIENCE PRIMERS, 



LOGIC. 

L— INTRODUCTIONo 

I. Monsieur Jourdain, an amusing person in one 
of Moliere's plays, expressed much surprise on 
learning that he had been talking prose for more than 
forty years without knowing it. Ninety-nine people 
out of a hundred might be equally surprised on hear- 
ing that they had long been converting propositions, 
syllogizing, falUng into paralogisms, framing hypo- 
theses and making classifications with genera and 
species. 

If asked whether they were logicians, they would 
probably answer. No ! They would be partly right ; 
for I believe that a large number even of educated 
persons have no clear idea what logic is. Yet, in a 
certain way, every one must have been a logician since 
he began to speak. 

It may be asked : — If we cannot help being 
logicians, why do we need logic books at all? 
The answer is that there are logicians and logicians. 
All people are logicians in some manner or degree ; 
but unfortunately many people are bad ones, and 
suffer harm in consequence. It is just the same in 
other matters. Even if we do not know the meaning 



8 ^ PRIMER OF LOGIC, [i. 

of the name, we are all athletes in some manner or 
degree. No one can climb a tree or get over a gate 
without being more or less an athlete. Nevertheless, 
he who wishes to do these actions really well, to have 
a strong muscular frame, and thereby to secure good 
health and personal safety, as tar as possible, shouH 
learn athletic exercises under a skilful teacher. 

2. To be a good logician is, however, far more 
valuable than to be a good athlete ; because logic 
teaches us to reason well, and reasoning 
gives us knowledge, and knowledge, as Lord 
Bacon said, is power. As athletes men cannot 
for a moment compare with horses or tigers or 
monkeys. Yet, with the power of knowledge, men 
tame horses and shoot tigers and despise monkeys. 
The weakest framework with the most logical mind 
will conquer in the end, because it is able to foresee 
the future, to calculate the results of actions, to avoid 
mistakes which might be fatal, and to discover the 
means of doing things which seemed impossible. If 
such little creatures as ants had better brains than 
men, they would either destroy men or make them 
into slaves. 

3. It is true that we cannot use our eyes or ears 
without getting some kind of knowledge, and the 
brute animals can do the same. But what gives 
power is the deeper knowledge called 
Science. People may see, and hear, and feel all 
their lives without really learning the nature of things 
they see. But reason is the mind's eye, and enables 
us to see why things are, and when and how events 
may be made to happen or not to happen. The logi- 
cian endeavours to learn exactly what this reason is 
which makes the power of men. We all, as I have 
said, must reason well or ill, but logic is the science of 
reasoning and enables us to distinguish between the 
good reasoning which leads to truth, and the bad 



ri.j REASONING. 



reasoning which every day betrays people into error 
and misfortune. 



II.— HOW WE COMMONLY REASON. 

4. The common way in which we reason is to ex- 
pect that things will happen as they have happened 
l3efore in like circumstances. Seeing a bright flash of 
lightning, I expect thunder to follow, because it has 
followed bright flashes of lightning in previous cases. 
When a bright yellow round fruit is offered to me I 
believe it to be an orange and eat it without hesita- 
tion, because fruit of exactly the same appearance 
had been eaten before without harm. The gold of 
Australia was discovered by this simple mode of 
reasoning. A man named Hargreaves remarked that 
the mountains of New South Wales were like those 
of California, where he had been digging gold, and he 
reasoned that being like in some respects, they ought 
to be like in other respects, and should contain gold. 
On making some trials he found that he was correct. 

5. But in this simple way of reasoning from like to 
like we may often deceive ourselves. When the things 
which we believe to be like each other are really so, 
no harm is done ; but things which seem to be like 
may be different : two kinds of fungus or two kinds 
of fruit may so closely resemble each other that I 
may not notice the difference ; yet one kind may prove 
to be wholesome to eat and the other poisonous. 
It is even possible that what looks exactly like an 
orange might be some new sort of fruit, and not an 
orange at all. 

People are so accustomed to use blankets to make 
themselves warm that they are surprised to see 
blankets used to keep ice cold, and to prevent it from 
melting. Expecting that the same thing will have the 



lo PRIMER OF LOGIC. [ii. 

same effect, they think that a blanket must make ice 
warm. But this would not really be a similar effect. 
What a blanket always does is to prevent heat passing 
from one side to the other. Thus it keeps the heat 
of the body from passing into the colder air around, 
and it keeps the heat of the air from passing into the 
colder ice. Housemaids, in trying to make a fire 
burn, sometimes reason badly. They stick the poker 
among the coals and leave it there, seeming to have a 
belief that the mere presence of the poker helps the 
fire to burn, because on some previous occasions the 
fire had burnt better when the poker was in it. They 
do not observe that the poker is only useful when so 
placed as to raise the coals and allow the air to enter 
freely. 

6. The truth is that only when things really are 
alike can we expect them to behave alike. The same 
causes have the same effects ; but the difficulty is to 
know when the causes are the same. To ascertain 
this requires more careful reasoning than we com- 
monly use. We need to discover what things go with 
other things always and everywhere as far as we can 
observe. We have to find out what are called the 
general laws showing what things will hap- 
pen under given circumstances. A fire some- 
times burns and sometimes does not burn. Then the 
circumstances must be different ; for a fire has no 
will ; and if one fire be laid and lighted exactly like 
another, it ought to burn like it. We must find out 
what things always favour the burning, such as the 
presence of abundant air, and the absence of moisture, 
and of any body which can carry much heat away. 
We shall thus learn that a cold poker put into a fire 
in one way will do more harm than good, by carrying 
away heat ; but, put in differently, it will do more 
good than harm, by admitting air and quickening 
combustion. 



II.] REASONING. II 

7. A general law of nature is something 
which is true of many objects, and science is 
made up of such laws. After reflecting a little, 
we shall see that logic ought to teach us to do two 
different things with respect to the laws of nature, 
namely, how to discover them, and how to use them 
when discovered. By inductive reasoning, as it 
is called, we ascertain what is true of many different 
things. Our eyes, and ears, and other senses tell us 
what happens around us, and then by proper reason- 
ing we may often discover the laws of nature, in 
consequence of which they happen. Observing that 
clouds, rain, snow, hail, dew, mist, and fogs, consist of 
water, which seems to come out of the air, we may, by 
a proper course of inquiry, discover that all moist air, 
when cooled in a certain degree, produces particles of 
water. We find that there is something the same in 
the causes of all these things. 

8. By deductive reasoning we do just the 
opposite, and from any law of nature we infer what 
will happen in consequence of it. To infer is to 
find out what will be true if something else 
is true. Knowing that moist air when cooled pro- 
duces particles of water, I may infer that an iced 
bottle of wine will in summer become covered with dew. 
Philosophers have discovered by induction that all 
bodies tend to fall towards the earth like stones ; then 
by deduction I can infer that the moon must tend to 
fall towards the earth. It may seem as if all the 
difliculty of reasoning lies in discovering laws by in- 
duction, and that we must certainly learn to discover 
the laws before we learn how to use them. The 
fact, however, is that we cannot possibly understand 
inductive reasoning unless we previouslv understand 
deductive reasoning. 

9. Before we can be said to know properly what a 
law of nature means, we must be able to see what it 



12 PRIMER OF LOGIC, [iii. 

leads to, that is, to infer its consequences. I cannot 
tell whether a law is true or not unless I see whether 
it agrees with what happens in nature. When philo- 
sophers came to the conclusion that all material 
bodies tend to fall towards the earth, they ought to 
have been able to foresee that the moon, being a 
material body, would tend to fall towards the earth, 
so as to inquire whether this was true or not. I 
shall afterwards show more fully that it is really by 
the use of deductive reasoning that we perform in- 
ductive reasoning. We will now proceed at once to 
consider what deductive reasoning consists in. 

III.— WHAT IS DEDUCTIVE REASONING.? 

lo. Let us take a simple case of reasoning, an argu^ 
ment, as it is often called, and consider in what way 
it is constructed. When we see a particular kind of 
white and pink fungus, and pluck it, because we 
believe it to be a mushroom, and we know that all 
mushrooms are good to eat, we certainly reason by 
an argument, which may be thus fully stated : — 

All mushrooms are good to eat ; 
This fungus is a mushroom ; 

Therefore, this fungus is good to eat. 

Here are three sentences which state three different 
facts ; but when we know the two first facts, we learn 
or gather the third fact from the other two. When we 
thus learn one fact from other facts, we infer or reason, 
and we do this in the mind. Reasoning thus enables us 
to ascertain the nature of a thing without actual trial. 
If we always needed to taste a thing before we could 
know whether it was good to eat or not, cases of 
poisoning would be alarmingly frequent. But the 
appearance and peculiarities of a mushroom may be 
safely learned by the eye or the nose, and reasoning 



II.]' REASONING, 13 



upon this information and the fact already well-known, 
that mushrooms are good to eat, we arrive without 
any danger or trouble at the conclusion that the 
particular fungus before us is good to eat. To 
reason, then, is to get some knowledge from 
other knowledge. 

II. Let us now examine more carefully the parts of 
which this argument about mushrooms is made up. 
There are three sentences, which put facts before us, 
and are therefore called Propositions. The first 
proposition tells us that ^^All mushrooms are good 
to eat," or, what means exactly the same, ^'All mush- 
rooms are things good to eat." This proposition has 
three principal parts. There are two descriptions of 
things compared together, namely, ^'mushrooms" and 
"thnigs good to eat." These kinds of things are 
mentioned, of course, by their names, and, as the 
name mushroom is at one end of the proposition, 
and things good to eat at the other end, these names 
are called the terms, or ends of the proposition. 
They are connected together by the little verb ^' are," 
which is called the copula or link. There remains, 
indeed, the little adjective "all," which tells us how 
many of the mushrooms are good to eat ; in the case 
of other things it might be few, or many, or none. 
In this case it is all, and we may call this the sign 
of quantity. 

The other propositions are made up nearly in the 
same way. Thus, in **This fungus is a mushroom," we 
observe two terms, namely, "this fungus," and "mush- 
room," which are connected together by the copula 
" is." In the third proposition, which we drew from the 
other two, the terms, "this fungus" and "thing good 
to eat," are found over again, with the copula "is." 
It will be observed that each term is used twice over 
in the argument ; "this fungus'' occurs in the second 
and third propositions ; " mushroom " in the first and 



14 PRIMER OF LOGIC. [iv, 

second; and ^^ thing good to eat" in the first and third. 
We learn firom our examination, that an ^argument of 
this kind consists of three propositions and of three 
terms, and that each proposition is made by joining 
two terms. When we join terms together we 
make a proposition ; when we join proposi- 
tions together we make an argument, or 
piece of reasoning. 

12. We should generally get nothing but nonsense 
if we were to put together any terms and any proposi- 
tions, and to suppose that we were reasoning. To 
produce a good argument we must be careful to obey 
certain rules, which it is the purpose of Logic to make 
known. But, in order to understand the matter 
perfectly, we ought first to learn exactly what a term 
is, and how many kinds of terms there may be ; we 
have next to learn the nature of a proposition, and 
the different kinds of propositions. Afterwards we 
shall learn how one proposition may by reasoning be 
drawn from other propositions in the kind of argument 
called the syllogism. Thus, there are three parts 
of Deductive Logic, which treat of Terms, 
Propositions, and Syllogisms. Terms and pro- 
positions are, indeed, merely the tools which we use 
in reasoning : but we cannot learn a trade unless we 
begin with learning the use of the tools employed in it. 
Hence we shall begin by considering the different 
kinds of terms and propositions before we go on 
to the syllogism. 

IV.— THE DIFFERENT KINDS OF TERMS OR 
NAMES, 

13. As we have already learnt, terms are the 
names of the things which we compare together in 
a proposition. Now names consist of what the gram 
mar books call nouns, and a single term may con 



IV. 1 TERMS. IS 

tain any number of nouns, substantive o/ adjective. 
Sometimes there is in each term only a single noun. 
Thus in " Diamonds are combustible/' the first term 
is the single substantive '' diamonds ^' ; the second 
term is the single adjective '' combustible." But a 
term will often be made of two or more nouns joined 
together in some way. The proposition " The Queen 
of England is the Empress of India " contains only 
two terms, but each of them is composed of two 
nouns, " Queen of England " being the first term, 
" Empress of India," the second. " The library of 
the British Museum is the greatest collection of books 
in the world." Here is a proposition containing fifteen 
words, yet it has only two terms ; the first is '' The 
library of the British Museum," in which we see two 
substantives, one adjective, two definite articles and 
one preposition ; the second is "the greatest collection 
of books in the world," in which we see three sub- 
stantives, one adjective, two articles, and two preposi- 
tions. A logical term, then, may consist of any 
number of nouns, substantive or adjective, with the 
articles, prepositions and conjunctions required to join 
them together ; still it is only one term if it points 
out, or makes us think of a single object, or collection, 
or class of objects. But there are several different 
kinds of terms, which we must next consider. 

14. Sometimes a term points out only a single 
person or thing, as " The Queen of England," *' The 
British Museum," " Pompey's Pillar." By the Queen of 
England we mean the present reigning Queen Victoria, 
and there is, of course, only one Queen Victoria. 
There is only one British Museum, and one single 
great obelisk called Pompey's Pillar. Hence terms 
of this kind are called singular terms, because each 
term is the name only of a single thing. 

15. The greater number of terms used in writing 
and speaking are, however, not singular but general 



i6 PRIMER OF LOGIC. [iv. 

terms. They are the names of things of which 
many exist. Thus ^' shilling " is not the name of any 
one single thing, like ^' Pompey's Pillar.'* There are 
many millions of things, each of which can be called a 
shilling ; and when I say that '^ all shillings are made 
of a mixture of silver and copper," I mean to state 
this of any and all the shillings. In the same way 
'^ horse '' is the name of any one of millions of horses 
which may exist m the world. The number of things 
denoted by a general term may vary from two or 
three to numbers exceeding anything that we can 
conceive. ^^ Present King of Siam " is the general 
term for either of the two existing kings of that 
country; ^' House of Parliament" is the general name 
either of the Lords or the Commons. '^ Grain of 
sand," is the name of any one of many billions, or 
even trillions of little particles ; and '^ particle of 
matter '* is a still wider general name; for all sub- 
stances which exist in the universe are composed of 
minute particles of matter. 

1 6. It may be remarked, indeed, that, as even a 
single thing, like Pompey's Pillar, is made up of 
many portions of matter, the name of the whole must 
be the name of all the parts. The continent of Asia 
is made up of many plains, lakes, mountains and 
rivers. Polynesia is the name of an immense number 
of islands scattered about the Pacific Ocean. Never- 
theless, each of these things is a single whole. There 
are not two Pompey's Pillars in existence, nor two 
Asias. nor two Polynesias. Hence each of these terms 
is a singular term, not a general term, and a singular 
term may be the name of many things, provided they 
are all put together into one single group or collec- 
tion. Polynesia is the name not of any one island, 
but of a great many islands in the Pacific Ocean. 
Such a term is called a Collective term, because it 
is the name of many things collected into one whole. 



IV.] TERMS. 17 

Library is the collective name for many books put 
together ; constellation, of many stars \ crowd, of 
many people. 

17. I have said that a general name is the name of 
many things ; but then, it is the name of any one 
of those things separately from the others. Thus 
" island " is the name of any one of the thousands of 
small pieces of land making up Polynesia. Island, 
then, is a general term ; Polynesia is a collective and 
singular term. The British Museum Library is the 
name of a great collection of books, not of any one 
of those books ; it is, therefore, a collective term, and 
is also singular. There are, however, a great many 
collections of books of various size in the world, 
so that tlie term '' Library," though it is collective 
as regards the books in any particular library, is 
yet general, because it is the name of any such 
collection. We thus see that the same term may be 
at once collective and singular, or collective and 
general ; but we must always take great care 
to avoid confusing collective terms with 
general terms. 

18. There is another difference between terms 
which it is not so easy to understand. Many terms 
are the names of solid objects, which we can touch 
or move about, and which exist by themselves, like a 
half-crown, a writing slate, or a brick house. Such 
terms are called Concrete terms, and they include 
most names which may be put in the plural ; thus we 
may speak of half-crowns, brick houses, mountains, 
planets, particles of matter, and so on. All these are 
concrete terms. 

Abstract terms, on the contrary, are names, not 
exactly of things, but of qualities which belong to 
things, as the thickness of a half-crown, the colour of 
a slate, the magnitude of a house, the elevation of a 
mountain. We cannot separate the thickness of a 
2* 



i§ PRIMER OF LOGIC. [iv. 

half-^rown from the half-crown, as we can separate 
one half-crown from another. Every obj ect has many 
quaUties ; a half-crown, besides thickness, has weight, 
sohdity, colour, ductihty, malleability, fusibility, con- 
ductibility, and many other quaUties, so that each of 
these terms is an abstract one. Properly speaking, 
an abstract term cannot be put into the plural. We 
ought not to speak of solidities, ductilities, fusibilities, 
these being perfectly abstract terms. It is true that 
we often speak of colours, weights, magnitudes : but 
it is probable that we then make the terms concrete. 
Altogether, there is much confusion between abstract 
and concrete terms, and the difference between them 
is not well understood. It will be sufficient to re- 
member that a concrete term is the name of a 
thing ; an abstract term is the name of a 
quality of a thing. 

19. We must now ascertain the difference between 
positive and negative terms. As a general rule 
we give a name to a thing because it has a certain 
quality. We call a house '* a brick house," because 
it is made of bricks ; black-lead is so called because 
it is black, and looks like lead. But in other cases 
we give a name to a thing for the opposite reason, 
because it has not got a certain quality. Thus we 
call a feat impossible, because it cannot be done ; 
a speech is unparliamentary when it does not agree 
with the rules of parliamentary debate ; an immense 
distance means a distance which has not been 
measured; an uneven surface is one not possessing 
evenness ; unfiltered water is water which has not 
been filtered. All these are negative terms. We may 
usually know a negative term by its beginning with 
one of the little syllables un-, in-, a-, an-, non-, or by 
its ending with -less. Thus unfavourable, indivisible, 
amorphous, anonymous, non-metallic, useless, are 
negative terms. But there are also many terms which 



IV.] TERMS. 19 



may be said to serve as negative terms, although they 
have no such mark at the beginning or end. When a 
piece of metal can be hammered out into a thin plate 
we call it malleable ; when it cannot be so ham.mered 
out, it might be called immalleable ; but this word 
has seldom been used, and we generally call such a 
piece of metal brittle. Thus *' brittle " serves as the 
negative term of ^* malleable." Similarly, opaque is 
the negative of transparent, false of true, dry of 
moist, rough of smooth, and so on. When we are 
speaking of written or spoken compositions, verse is 
the negative of prose, and prose the negative of verse, 
unless, indeed. Monsieur Jourdain was right in think- 
ing that he could get a love-letter written neither in 
verse nor in prose. 

20. If the English language were a perfect one, 
every term ought to have a negative term exactly cor- 
responding to it, so that all adjectives and nouns 
would be in pairs. Just as convenient has its negative 
inconvenient; metallic, non-metallic; logical, illogical ; 
and so on; so blue should have its negative non-blue; 
literary, non-literary ; paper, non-paper. But many of 
these negative terms would be seldom or never used, 
and, if we happen to want them, we can make them 
for the occasion by putting not-, or non-, before the 
positive term. Accordingly, we find in the dictionary 
only those negative terms which are much employed. 
When we are speaking in England of those belonging 
to Christian sects, a Churchman means one belonging 
to the Church of England. Those who, being Chris- 
tians, are not Churchmen, are called Dissenters, so 
that the term Dissenter serves as the negative of 
Churchman. But we have no separate names for 
those who are not-Wesleyans, or not-Methodists, or 
not- Baptists. 

Sometimes the same word may seem to have two 
or even more distinct negatives. There is much 



20 PRIMER OF LOGIC. [v. 

difference between undressed and not-dressed, that is 
"not in evening dress.'' Both seem to be negatives 
of " dressed," but this is because the word has two 
distinct meanings. 

21. Mistakes frequently arise from not observing the 
distinction between negative terms which indicate the 
complete absence of some quality, and comparative 
or opposite terms which only mean various degrees of 
the property. Thus the term '^ small'' is not really 
the negative of "- large," because there may be things 
which are neither large nor small, that is, are of 
medium size. The negative of large is not-large, 
which includes both medium and small; similarly, the 
negative of small is not-small, which includes both 
medium and large. So with warm and cold, light and 
dark, heavy and light ; these are not pairs of positive 
and negative terms, unless by cold we mean the entire 
absence of warmth, by dark the entire absence of light, 
and so on, as we seldom do. We never can make 
anything so cold that it contains no heat at all ; the 

' question is altogether one of degree. Thus the word 
'' hot,'' as we generally use it, does not mean ^'possessing 
heat," the negative of which would be " not possessing 
heat," but '* possessing more than medium heat," 
the negative of which is '^ not possessing more than 
medium heat," and includes both things which are of 
medium temperature and those which would be called 
cold. If then a person denies that a thing is hot, he 
ought not to be understood as asserting that it is cold, 
for it may be just short of being hot, and yet not cold. 

v.— THE FULL MEANING OF TERMS. 

22. We cannot really form a clear notion of what 
a concrete term means unless we observe that there 
are two different kinds of meanings, namely, the 
things to which the term is applied, and the 



v.] TERMS, 



qualities of those things in consequence of 
which it is applied. When I see a large peculiar- 
shaped iron structure floating on the water with masts 
and sails, I call it a ship, because it is evidently 
adapted to sailing and conveying goods and pas- 
sengers. Every other structure having the same 
general appearance and purpose I also call ship, and 
if I were asked Why, I should have to answer as 
best I could, that every large vessel made to move 
through the water easily and convey things is a ship. 
Whenever, then, I call a thing a ship I must mean 
that it has these peculiarities ; it is these circumstances 
which make it a ship, and lead me to use the name 
ship ; so that the word means that the thing to which 
it is appHed is made to move easily through the water, 
and so forth. But, on the other hand, the name ship 
is the name of the thing, and there are a great many 
particular ships, such as the Great Britain^ the Great 
Eastern^ the Challenger^ the Castalla, the Minotaur, 
the Vanguard. 

In reality every ordinary general term has a double 
meaning : it means the things to which it is applied, 
for instance, the particular ships named : it also means 
in a totally different way, the qualities and peculiarities 
implied as being in the things. Logicians say that 
the number of things to which a term applies is the 
extension of the term ; w^hile the number of quali- 
ties or peculiarities implied is the intension. 

23. When we compare together terms which are 
partly different and partly the same, we shall find 
that they have various degrees of extension and in- 
tension. Take, for instance, the term " ship " and 
compare it with "steam-ship." There are evidently 
many more ships than there are steam-ships, because 
we have in the meaning of the latter term to exclude 
saihng ships. Hence m putting steam before ship we 
have greatly reduced the extension of the term. But 



22 PRIMER OF LOGIC, [vi. 

we have increased its intension, because steam-ship 
means all that ship does, and more, for it means 
that the ship is moved by steam power. Put another 
word before it and compare screw-steam-ship with 
steam-ship, and we find we have again reduced the 
extension, by putting out of sight the steam-ships yet 
propelled by paddles ; these are comparatively few 
in the present day, so that we have not made any 
very great difference ; but we have nevertheless in- 
creased the intension of meaning considerably, because 
we know precisely in what way a thing called a screw- 
steam-ship is moved. War-screw-steam ship is a still 
narrower term, that is, has much less extension, 
because it now applies only to those ships owned by 
a government for war purposes ; but this makes an 
addition to the intension or the circumstances and 
quahties implied. British-war-screw-steam-ship is in 
like manner a still narrower term, and we might go on 
further specifying that it is iron clad, that it is in 
commission, is in the Channel Fleet. We have thus 
narrowed the extension so much that there may only 
be half-a-dozen ships to which our description will 
now apply. If we add that it bears the AdmiraFs 
flag, this removes all but a single ship, so that the 
extension is reduced to the least possible. At the 
same time the intension becomes very great, and if 
we happen to be acquainted with the ship, and to 
have heard much about it, all the knowledge which 
we have of the ship is suggested by the name. 



VI.— THE CORRECT USE OF WORDS. 

24. In endeavouring to reason correctly, there is 
nothing more necessary than to use words with care. 
The meaning of a word is that thing which 
we think about when we use the word, and 



VI.] USE OF WORDS. 23 

which we intend other people to think about when 
they hear it pronounced, or see it written. We can 
hardly think at all without the proper words coming 
into the mind, and we can certainly not make known 
to other people our thoughts and arguments unless we 
use words. Yet there is no more common source of 
mistakes and bad reasoning than the confusion which 
arises between the different meanings of the same 
word. 

25. Take for instance the word ^'church." It 
may, no doubt, be said to mean the solid building of 
stone or brick, to which people go to worship, and 
when used in this sense there can seldom be any 
important mistake. But it is also common to speak 
of the Church as meaning the whole body of people 
who worship in a particular manner, and have the 
same creed and ritual. Thus there is the Church of 
England, the Church of Rome, the Greek Church, 
the Free Church of Scotland, and so forth. When 
we say a person has gone over to the Church of 
Rome, we do not mean that he has gone bodily to 
Rome, but that he has simply changed his belief. 
Each different sect too speaks of the Church as mean- 
ing their own Church, so that two people arguing 
together and speaking of the C» au'ch may mean totally 
different Churches. 

26. There is, however, a still more serious confusion 
in the meanings of the word, because the bishops, 
clergy, and other authorities of the Church, being 
the most prominent members of it, and governing, 
representing, and expressing the opinions of the 
Church, often come to be spoken of as if they were 
the Church. Properly speaking, the congregation 
who attend worship have as much right to be con- 
sidered part of the Church as the clergy, and they 
have, to a certain extent, the right of electing officers, 
of deciding questions about the building, and so forth. 



24 PRIMER OF LOGIC. [vi. 

But, if we include the congregation, how are we xo 
decide who shall be counted as proper members? 
Not everybody who goes inside a church door can be 
called a member of the Church. For some purposes 
we should include only regular communicants; for 
other purposes those who have been baptized, and 
confirmed, and not excommunicated ; many overlook 
the confirmation, and there may be persons who, 
without having been even baptized, consider them- 
selves members of a Church, because they have re- 
gularly attended worship, and have subscribed towards 
the expenses. Even while we are discussing the 
word " church," it is difficult to avoid speaking more 
in reference to some one Church, for instance, the 
Church of England, than to other Churches. We 
must remember that the Wesleyan, Baptist, Roman 
Catholic, and many other Churches, take much care 
to ascertain and settle, who do, and who do not 
belong to their particular Churches. 

27. In many cases the meanings of a word are so 
distinct that they cannot really lead us into more than 
a momentary misapprehension, or give rise to a pun. 
A rake may be either a garden implement, or a fast 
young man ; a sole may be a fish, or the sole of the 
foot ; a bore is either a tedious person, a hole in a 
cannon, or the sudden high wave which runs up some 
rivers when the tide begins to rise ; diet is the name 
of what we eat daily, or of the Parliament which 
formerly met in Germany and Poland ; ball is a 
round object, or a dance. In some cases a word is 
really a different word in each of two or three mean- 
ings, and comes from quite different words in other 
languages. Thus, bale is the name of a bundle or 
package of goods, and seems to be derived from the 
same French or Latin words as ball; but bale is also 
an old name for evil, calamity, or sorrow, and in this 
meaning comes from an altogether distinct root. The 



/I.] USE OF WORDS, 25 

corn which we eat is the Latin gramcm^ but a corn 
or horn on the foot is the Latin cornii. Bill 
means either William, a document, or a hooked 
object, for instance, the bill of a bird. In each case 
it is really a different- word similarly spelt. From 
such confusions of words puns and humorous mistakes 
may arise, but hardly any important errors. 

28. In most cases a word changes its meaning by 
degrees, and we use it for anything which is close 
xo, or connected with, the first meaning. A bench 
means a board to sit on, but " the bench " is a 
common expression for the row of magistrates sitting 
on the bench. A board means a broad flat piece of 
wood, but being often used to support the dishes at 
a meal, people speak of the food itself as the board. 
Again, because a small meeting of men often sit 
round a table for convenience, they are sometimes 
called a board, as in the Board of Trade, and a small 
meeting-room is very commonly called a board-room. 

29. Any word which has two or more meanings, 
and is used in such a way that we are Hkely to con- 
fuse one meaning with another, is said to be am- 
biguous, or to have the quality of ambiguity. By 
far the greater number of words are ambiguous, and 
it is not easy to find many words which are quite free 
from ambiguity. Whether we are writing, or reading, 
or speaking, or merely thinking, we should always be 
trying to avoid confusion in the use of words, but no 
one can hope to avoid making blunders and failing 
into occasional fallacies, as we shall learn in a later 
part of this Primer. 

30. In many important cases it seems almost im- 
possible to decide exactly what a name means. 
House, for instance, has a great many meanings. No 
doubt, it first meant any kind of roofed building in 
which people live ; but, as the shelters made for cows 
much resembled houses, they were called cow-houses ; 



26 PRIMER OF LOGIC, [vi. 

and we speak now of ice-houses, tool-houses, green- 
houses, hot-houses, bathing-houses, wash-houses, and 
many other kinds of houses, in which no hving beings 
remain long. Counting-houses, again, bemg the 
chambers in which men conduct business, we often 
speak of the house instead of the men, just as we 
speak of the bench instead of the magistrates. 
Thus a commercial house means a firm, or partner- 
ship, or company doing business together. i\s mem- 
bers of Parhament need chambers to meet and debate 
in, there is the House of Lords, and the House of 
Commons, and it is usual to speak of ^' The House " 
meaning the collection either of Lords or Commons 
who happen to be present. Here again there is 
ambiguity ; for the House of Commons may mean 
either the members who happen to be in the House 
at any particular moment, or the whole body of 652 
members whose right and duty it is to be there when 
the Speaker is sitting. 

' 31. Even beyond all these varieties of meaning, 
there is further uncertainty as to what house means 
when it is merely a dwelling-house. Houses are of 
various sizes, and if a family live in a building having 
only one single chamber, it would be a house. 
Legally speaking, the head of the family would be 
a householder. If several poor families divide a large 
house between them, each taking one or two rooms, 
we still speak of the whole building as one house. 
Nevertheless, it is for practical purposes made into 
several houses. If a single room standing alone 
makes a house, as in the case of many cottages, why 
should not single rooms inhabited by different families 
under the same roof make different houses? Whether 
there is or is not an outer front door is not a matter 
of real importance. If in this way we follow out our 
use of the word house, we shall find that we cannot 
give a satisfactory account of it. 



VII.] CLASSIFICATION. 27 



VII.— HOW AND WHY WE CLASSIFY THINGS. 

32. The larger number of terms, as we have learnt 
in Art. 15, are the names, not of single objects, but 
of many objects, or rather of any one of many 
objects. ** Man " is the name of any one of many 
hundreds of millions of men, living or dead. We 
have hitherto called such names, general names 
or terms ; but we may now say that they are the 
names of classes of things, provided that we 
take great care to ascertain exactly what we mean by 
a class. 

W^e class things together whenever we 
observe that they are like each other in any 
respect, and therefore think of them to- 
gether. Milk, chalk, snow, meerschaum, paper, mist, 
spray, foam of the sea, pearls, and white lead, are 
very different things in most points, but they all agree 
in being white. Together with many other substances 
and things, they are put together in thought into the 
class of white things. In this case the resem- 
blance is only in regard to colour ; but in other cases 
there may be many points of resemblance. 

The class of things called '^pens," for instance, 
includes things made of quills, reeds, steel, gold, 
silver, glass, and some other substances ; the forms of 
pens also differ \ nevertheless, they are all Hke each 
other in being made to hold fluid ink, and to spread 
?t over paper. 

33. There is nothmg more useful than to be able 
to classify things correctly and easily, and to form 
exact general notions about them. So far as things 
are exactly alike, whatever is true of one 
thing will be true of the others, which so 
resemble each other. When we classify 
things correctly, we ascertain the exact 



28 PRIMER OF LOGIC, [vii. 

nature and degree of their resemblances, and 
record the information we have gained in 
the briefest and most convenient form. Our 

knowledge is increased to the utmost, and, instead of 
being obliged to remember an immense number of 
disconnected facts, we have only to comprehend a 
comparatively small number of general truths. To 
take a very simple case, we class together white things 
because they all act in the same way with respect to 
light. Linen, snow, chalk, cloud, and porcelain, are 
exceedingly different in other respects, so that it is 
only with regard to light that we expect the same fact 
to be true of all of them. Those who walk over a 
large extent of snow when the sun is shining, find 
their eyes painfully affected by the glare of the light 
reflected from the snow. They might expect therefore 
that the same effect would follow from walking over 
a large extent of ground covered with white chalk, 
white dust, or white linen laid out to bleach in the 
sun. Again, when we want to reflect light we shall 
know that we ought to use white substances; in a 
dark room we should have a white ceiling, and white 
paper or paint on the walls. If there be walls in 
front of a window, they should be built of white-faced 
bricks, or covered with white-wash, if we want ad- 
ditional light in the room, and white bricks are often 
used for this purpose at the present day. Sometimes, 
too, whiteness will assist us in avoiding the effects of 
the excessive intensity of the sun's rays ; people in 
tropical countries wear white clothes and hats with 
this object, and roofs are sometimes white- washed in 
order that they may absorb less of the sun's heat. 
All these results follow from the one general truth or 
law that white things reflect rays of light. 

34. The studies of botanists and other naturalists 
are chiefly directed to classifying plants and animals 
in the most perfect manner, because it is only by 



vii. ] CLASSIFICA TION. 29 

classification that we can possibly remember or un- 
derstand the characters of the immense numbers of 
living things. All kinds of grasses, including wheat, 
barley, oats, and other kinds of corn, belong to one 
very well-marked class. -Any one having a moderate 
knowledge of botany can tell with ease whether a 
given plant is a kind of grass or not. Now the food 
both of men and brutes is chiefly derived from some 
sort of grass, and it is believed with much reason that 
no plant belonging to the class is poisonous. Hence 
a traveller in want of food in an uninhabited country 
might always eat the seeds of any kind of grass 
without fear. On the other hand, plants belonging to 
the order Lobeliacece should never be eaten, as most if 
not all of them are dangerously poisonous. The same 
may be said of the flowers and berries of plants 
belonging to the order of Solanacece^ among which 
is the Deadly Night-shade. A good botanist would 
know, almost at a glance, that these and many other 
classes of plants were to be avoided, or very carefully 
used. 

35. It is somewhat the same with classes of sub- 
stances or living beings. The properties of the class 
"man" are exceedingly numerous. The surgeon who 
has well studied anatomy knows almost exactly the 
form and place of every bone, tendon, muscle, nerve, 
gland, or other organ. There are various circum- 
stances in which one man may differ from another; 
these are in logic called accidents. An organ or 
muscle may be smaller or larger in one man than 
another; but it will be present in all, so that the 
possession of the organ is a property of the man. 
Chemical substances, again, have innumerable well- 
marked properties. If a chemist meets with a trans- 
parent colourless cr}^stal, and decides by certain 
tests that it is composed of carbonate of lime, he 
knows at once how it will behave, if treated with 



30 PRIMER OF LOGIC, [vii. 

various acids, or if burnt in the fire ; for he knows 
the properties which belong to all portions of *car- 
bonate of lime. 

36. In classifying things, however, we must take 
great care not to be misled by outward resemblances. 
Things may seem to be very like each other which 
are not so. Whales, porpoises, seals, and several 
other animals live in the sea exactly like fish ; they 
have a similar shape, and are usually classed among 
fish. People are said to go whale-fishing. Yet these 
animals are not really fish at all, but are much more 
like dogs and horses and other quadrupeds than they 
are like fish. They cannot live entirely under water 
and breathe the air contained in the water like fish, 
but they have to come up to the surface at intervals 
to take breath. Similarly, we must not class bats 
with birds because they fly about ; although they have 
what would be called wings, these wings are not like 
those of birds, and in truth bats are much more like 
rats and mice than they are Hke birds. Botanists 
used at one time to classify plants according to their 
size, as trees, shrubs, or herbs, but we now know that 
a great tree is often more really similar in its character 
to a tiny herb than it is to other great trees. A daisy 
has little resemblance to a great Scotch thistle ; yet 
the botanist regards them as very similar. The lofty 
growing bamboo is a kind of grass, and the sugar- 
cane also belongs to the same class with wheat and 
oats. 

37. In classifying a collection of objects, we do 
not merely put together into groups those which re- 
semble each other, but we also often divide each 
larger class into smaller ones, in which the resemblance 
is more complete. Thus, the class of white substances 
may be divided into those which are solid and those 
which are fluid, so that we get the two minor classes 
of solid white, and fluid white substances. It is 



VII.] CLASSIFICA TION, 



desirable to have names by which to show that one 
class is contained in another, and accordingly we call 
the class which is divided into two or more smaller 
ones, the genus, and the smaller ones into which it 
is divided, the species. Solid white substance is a 
species of the genus white substance. If house be 
taken as a genus, then dwelling-house would be a 
species. But, when we like, we can again turn the 
species into a genus, by dividing it up a second time 3 
thus, brick dwelHng-house would be a species of the 
genus dwelling-house. This we might do again and 
again, getting, for instance, the still smaller species, 
new brick dwelUng-house, large new brick dwelling- 
house, Elizabethan large new brick dwelling-house, 
and so on, almost without limit. 

38. It is often a difficult question to decide how, in 
any particular case, we can best divide up a large 
class into smaller ones. The common way is to make 
as many species all at one step, as there are kinds of 
things belonging to the class, which we can think of 
at the time. Thus, we might divide boats into saiUng- 
boats, steam-boats and row-boats. Beasts of burden 
might be divided into horses, mules, donkeys, camels, 
and elephants. Books might be divided into those 
which treat of History, Geography, Biography, General 
Literature, the Physical and Moral Sciences, the 
Arts, Political Economy, Theology, Poetry, Fiction, 
Periodical Publications, &c. But, in making such 
classifications, we are almost sure to fall into logical 
blunders. 

39. In the first place the species or small classes 
are likely to overlap each other, unless we make the 
divisions with much care. If we divide the people of 
England into men, women, children, paupers, vagrants, 
blind, deaf and dumb, and foreigners, we commit 
several very evident blunders, because paupers, Wind, 
deaf and dumb, as well as foreigners, must be either 



32 PRIMER OF LOGIC, [vii. 

men, women, or children, so that if they were 
counted once in that respect they ought not to be 
counted again as paupers, bUnd persons, &c. Vagrants 
are a kind of paupers, and often difficult to distinguish 
from them. Moreover, vagrants and foreigners may 
happen to be blind, or deaf and dumb. In dividing 
books, again, it will be found impossible to make any 
classification in which a book shall always belong to 
one species and only to one. The species will be 
sure to overlap. There may be books on the history 
of science which might be equally well placed in the 
class of histories, or in that of books on physical 
science. There may be books which are half bio- 
graphy, half history. Miss Martineau's *^ Tales on 
Political Economy," might be placed both in the class 
of fiction and in that of political economy. Nobody 
can be sure in which class any particular book will be 
found, and accordingly such classifications are not 
only logically bad ones, but they are of little use. 
Yet we find them employed in the catalogues of many 
libraries. 

40. A second difficulty is, that, in planning such 
classifications, we can seldom be sure of making 
enough species to include all the things belonging^ to 
the genus. There may be beasts of burden which 
are neither horses, mules, donkeys, camels, nor ele- 
phants ; for instance, the llamas used in South 
America, yaks in Thibet, and oxen in many parts of 
the world. Boats need not always be comprised 
under sailing-boats, steam-boats, and row-boats ; thus, 
there are boats with paddle-wheels worked by a 
handle or crank inside the boat ; there are also canal- 
boats towed by horses or men, ferry-boats moved by 
the force of a river, barges which go up and down 
with the tide in a river. 

41. All these difficulties are avoided in the per- 
fect logical method of dividing each genus 



vn. ] CLASSIFICA TION. 33 

into two species and not more than two, so 
that one species possesses a particular quality, 
and the other does not. Thus, if I divide dwell- 
ing-houses into those which are naade of brick and 
those which are not made of brick, I am perfectly safe, 
and nobody can find any fault with me. Even if I do 
not know what dwelHng-houses are exactly, yet I may 
be quite sure that anything which is a dwelling-house 
will belong either to the species made of brick, or, if 
not, to the other species which are not made of brick. 
But this would not be the case if I divide the genus 
at one step into many species. Suppose, for instance, 
that I divide dwelling-house as below ; — 
Dwelling- H ouse. 

\ \ i i 

Brick. Stone. Earth. Iron. Wood. 

The evident objection will at once be made, that 
houses may be built of other materials than those 
here specified. In Australia houses are sometimes 
made of the bark of gum trees ; the Esquimaux live 
in snow houses ; tents may perhaps be considered as 
canvas houses, and it is easy to conceive of houses 
made of terra-cotta, paper, straw, &c. All logical diffi- 
culties will however be avoided if I never make more 
than two species at each step, in the following way: — 
Dwelling- House. 

I ; 

Brick. Not-brick. 

I 



Stone. Not-stone. 

I 



Wooden. Not-wooden. 



Iron. Not-iron. 



34 PRIMER OF LOGIC. [vii. 

It is quite certain that I must in this division have 
left a place for every possible kind of house \ for if a 
house is not made of brick, nor stone, nor wood, nor 
iron, it yet comes under the species at the right hand, 
which is not-iron, not-wooden, not-stone, and not- 
brick. 

42. If, again, we divide substances into the two 
species, solid and not solid, every substance must fall 
into one or the other, and nothing can fall into both. 
No doubt there are degrees of solidity, and we might 
meet with substances such as tar, treacle, putty, &c., 
which might be said to be in a half solid state. But, 
if they are only half solid they must not be put into 
the class of solid things, and therefore they must go 
into the class of things which are not solid. If 
requisite we may make a new class of viscid things, 
or semi-fluid things, and we may go on, time after 
time, making divisions in the same way. We should 
get some such series of divisions as the following : — 

Substance. 





1 


Solid. 


1 
Not-solid. 

1 




! I 
Viscid. Not-viscid. 

1 




.1. 1 

Liquid. Not-liquid. 



r 

Gas. Not-gag. 

We must understand, in reading the above, that 
liquid things are both not viscid and not solid, and 
that gas is not liquid, not viscid, and not solid. No 
possible logical fault can be found with this ; for, if 
we really know what we mean by a solid, viscid, 
liquid, and gas, any substance whatever must fall 



VII.] CLASSIFICATION. 35 

under one division and only one. If we can find any 
substance, such as india-rubber or jelly, which does 
not correspond to any of the descriptions of solid, 
viscid, liquid, or gas, there still remains a division 
provided for it, namely, that of not solid, not viscid, 
not liquid, not gas. 

This manner of classifying things may seem to be 
inconvenient, but it is in reality the only truly logical 
wayc Other methods of dividing a genus into species 
are only correct so far as they are constructed on the 
same principle, though this may not be apparent. 

43. Let us inquire exactly what we do when we 
take brick-dwelHng-house as a species of the genus 
dwelling-house. There are certainly not so many 
brick-dwelhng-houses as there are dwelling-houses, 
because we exclude from the species all stone, wood, 
iron, or other kinds of dwelling-houses. Thus we find 
that the species has a narrower extension 
than the genus (Art. 22). In one way it has less 
meaning than the genus, because there are fewer 
objects called brick-dwelling-houses, than those which 
may be called dwelling-houses. But in another point 
of view there is more meaning in the species than 
in the genus, because we know more about the things. 
We know that anything placed in the class brick 
dwelling-house is not merely a dwelling-house, but 
that it is made of bricks. This we may express by 
saying that the species has greater intension 
than the genus, meaning by intension (Art. 22) 
the number of qualities which belong to all things in 
the class. 

44. The quality by which a genus is divided into 
two or more species is called the difference. In 
the last article, brick, or "made of brick," is the 
circumstance by which the species of brick-dwelling- 
houses is distinguished from all other dwelling-houses. 
Thus we may be said to add the quality " made of 



36 PRIMER OF LOGIC. [vii. 



brick " to the qualities of a dwelling-house, in order 
to get the qualities of the species we want. These 
qualities, namely those common to all of the genus, 
with the difference added, make the definition of the 
species. By a definition we mean a precise 
statement of the qualities which are just 
sufficient to mark out a class, and to tell us 
exactly what things belong to a class and what do 
not. Nothing is more important than to be able to 
define clearly the classes of things about which we 
are debating, but this is often a difficult task. In 
this case the definition of brick-dwelling-house, will 
consist of the difference, ''brick," added to the de- 
finition of dwelling-house, which again might be said 
to consist of the circumstance that the house is used 
for dwelling in, added to the definition of a house. 

45. We must not suppose for a moment that all 
the qualities of a thing are to be included in its 
definition. A certain qualily may belong to some 
of a class and not to others, in which case it obviously 
cannot be part of the definition. Some bricks are 
red, some white, and some blue ; the quality redness, 
then, will be no part of the definition of brick-dwelling- 
house, but will be said to be an accident of the 
species. Thus by an accident we mean any quality 
or circumstance which may or may not belong to a 
class, accidentally as it were. There are other qualities 
which belong to the whole of a class and yet are 
not regarded as part of the definition. Such quali- 
ties are called properties of the class. We 
might perhaps say that it is a property of all brick 
dwelling-houses to be durable. It is a property of 
the class mushroom to be good to eat ; it is a pro- 
perty of all the large class of grasses to be not 
poisonous. 

46. It will now be understood how important it is 
to be able to classify and define things accurately, 



viii.] PROPOSITIONS, 37 

because when once we can do this, the properties 
which belong to the things will also be readily known. 
The qualities of the things which we meet with around 
us are not mixed up without order, but some of them 
follow from or are attached to other qualities. This 
is very well seen in the case of geometrical figures. 
We define the species triangle, as containing " three- 
sided rectilinear figures. '^ The genus is rectilinear 
figure, or '* figure made entirely of straight lines," and 
the difference is ^^ three-sided,'^ by which triangles are 
distinguished from figures of four, five, or more sides. 
But triangles besides being three-sided rectilinear 
figures have many other properties always present. 
The three angles of a triangle, when added together 
always make exactly two right angles. If lines be 
drawn through the middle of each side of a triangle 
perpendicularly to the side, they will all meet in one 
point, and so will lines drawn through the angles, and 
dividing them equally. There are a great many other 
circumstances true of all triangles, as may be learnt 
in any book on geometry, and all these may be 
rightly called properties of triangles. A circle may 
be defined as a plane figure, every point in the 
boundary of which is equally distant from a single 
point, but the properties of circles are exceedingly 
numerous, and are not fully described in any book 



VIII.— PROPOSITIONS. 

47. Having now suflftciently learnt the nature and 
use of logical terms, we come to the second part ol 
logic, which describes propositions. As we learned at 
the beginning (Art. 11), an ordinary proposition joins 
two terms together by means of a verb called a 
copula. It is only when we thus assert some agree- 
ment or connection between terms, or assert one 



38 PRIMER OF LOGIC. [via. 

thing of another that we can be said to be right or 
wrong. If I were to say *' The weather " without 
saying anything more, no one could know what I 
meant, or whether I meant anything at all. Nobody 
could answer me, or say that I was either right or 
wrong. But, if I say "" The weather is hot '" people 
can judge whether there is an agreement between 
the terms corresponding with what they feel Let 
us mquire exactly what is the meaning of a proposi- 
tion. 

Take as an example '^ Coins are metallic." Here 
we have one concrete general term, Coins, joined to 
another concrete general term, metallic, which may be 
considered to mean ^' made of metal." The proposition 
states that the quality of being made of metal belongs 
to all coins. The things about which we are chiefly 
thinking are coins, and the term coins is therefore 
said to form the subject of the proposition. In 
most cases we may know the subject of a proposition 
by its being put first. The copula '*are" comes next, 
and joins the subject to words indicating the quality 
which belongs to it, namely "" metallic.'' This is called 
the predicate of the proposition, which is merely 
a word derived from the Latin, and meaning that 
which is stated or affirmed. A proposition 
consists, then, of subject, copula, and predicate in the 
order as thus stated. 

48. We may explain the meaning of a proposition 
in another way, which, however, comes to the same 
thing in the end. There are great numbers of coins 
in the world, and still greater numbers of things made 
of metal. When we say '* Coins are made of metal," 
we assert that all coins will be found among the 
things made of metal. If we could imagine all the 
metallic things in the world put into a heap together, 
and if we then picked the coins out of them, we should 
get all possible coins, because, if there were any not 



VIII.] PROPOSITIONS, 39 

in the supposed heap, they would not be made of 
metal, all things so made having been put into this 
heap. We come to this result then, that a proposition 
of the kind described asserts that the subject is 
the name of a thing, or class of things, con- 
tained among the more numerous things of 
which the predicate is the name. 

49. I have said that a proposition consists of sub- 
ject, copula, and predicate joined together in the 
order as stated. But they are not always given in this 
way in writing and speaking. Sometimes the propo- 
sition is inverted and the predicate is put first, as in 
''Blessed are the peacemakers," '^ Strong is truth." 
In such cases we must judge as well as we can which 
is the subject and which the predicate by the charac- 
ter of the words or their meanings. Thus the words 
'•' blessed " and *• strong " being both adjectives are 
evidently predicates. Very commonly, again, the 
copula is not distinctly expressed but is contained in 
a verb. *' The sun shines " seems to be a proposition 
with two terms and no copula, but it really means 
"The sun is shining." In Latin a single verb may 
make a complete proposition, as in "Amo," I love. 
When Caesar said " Veni^ Vidi, Vici," I came, I saw, 
I conquered, he expressed three complete propositions 
in three words. The science of language, however, 
shows that each of these single words arose from the 
joining together of the subject, copula, and predicate, 
in the same way that we shorten " I am " into " I'm," 
or "do not" into "don't." 

50. There are, however, various kinds of proposi- 
tions, and that as yet considered belongs to the 
affirmative kind. Negative propositions, on 
the contrary, assert that the subject is not con- 
tained among the predicate. When I say 
'' Coins are not combustible " I think at the same 
time of two classes of things, '^ Coins " and " com- 



40 PRIMER OF LOGIC, [vii\. 

bustible things;" but I come to the conclusion that 
the coins would not be found among combustible sub- 
stances, such as wood, coal, oil, gas. If we had a 
museum which contained nothing but combustible 
things, there would not be a single coin shown in it. 
Similarly, in a museum of coins we shall not find an\ 
combustible thmg shown as a coin. Thus the nega- 
tive proposition in question asserts that the subject 
and predicate are altogether separate, and that no 
object belonging to the one class is found likewise in 
the other. We may know a negative proposition by 
its containing the little word "not," or it may be 
"no;" but sometimes such words as "never'' or 
" nowhere " are used to make negative propositions. 

51. So far it has seemed as if there were only two 
kinds of propositions, affirmative and negative. But, 
before we go on, I ought to say that propositions may 
be divided in a quite different way. Hypothetical 
propositions do not positively assert the predicate of 
the subject, except under certain circumstances. Thus, 
" if water be boiling, it will scald " is a hypothetical 
proposition asserting, not that all water will be found 
among scalding things, but that, when it is boiling, it 
will scald. " If gunpowder be damp, it will not ex- 
plode ; " this is a negative hypothetical pro])osition ; 
for it asserts that gunpowder, when it happens to be 
damp, will not be found among exploding things. 
Hypothetical propositions may generally be recognised 
by containing the little word " if; " but it is doubtful 
whether they really differ much from the ordinary 
propositions already considered. We may easily say 
"boiling water will scald," and " damp gunpowder will 
not explode," thus avoiding the use of the word "if." 

52. Propositions belonging to a third class are 
called disjunctive, and contain the Httle conjunction 
"or," sometimes together with "either." As exam- 
ples we may say: "Lightning is sheet or forked;" 



VIII.] PROPOSITIONS. 41 

** Arches are either round or pointed ; " *^ Angles are 
either obtuse, or right angled, or acute." These pro- 
positions, as we see, contain more than one predicate, 
and do not say to which the subject belongs. Arches 
are not always round, arid if not round are pointed, 
and if not pointed they are round. There is a choice 
of predicates. Disjunctive propositions are very im- 
portant, but more difficult to understand than other 
kinds of propositions, and it will be convenient to 
leave their further consideration until after we have 
learnt the nature of syllogistic reasoning. 

53. We have already learnt that propositions may 
be affirmative or negative. They differ also as regards 
what is called the quantity of the proposition, 
which depends upon the quantity of the subject of 
which the predicate is held to be true. When I say 
'^ AU clouds in the sky are composed of particles of 
water " I mean to assert that the whole quantity of 
clouds appearing high up in the atmosphere are to be 
found among things composed of minute particles of 
water. There are other things also formed of such 
particles, namely mists, fogs, spray, steam, &c. I may 
say then that the predicate in this proposition be- 
longs universally to all clouds in the sky, and the 
statement is accordingly called a universal pro- 
position. 

54. If I say again, ** Some persons are deaf-mutes," 
the quantity of the subject persons is said to be parti- 
cular, because, as shown by the little adjective "some," 
I do not intend to assert that more than a portion of 
the subject ^* persons" are known to be in the class 
of deaf-mutes. Every proposition in which the pre- 
dicate is stated to belong to a part of the subject is 
called a particular proposition. As other in- 
stances I may mention such as the following : " a few 
Englishmen can speak Chinese ; " " m.any Englishmen 
emigrate ; " " certain books are intended only for 



42 PRIMER OF LOGIC, [viii, 

■ y 

reference ; " " most storms are preceded by a fall of 
the barometer." Particular propositions may be either 
negative or affirmative ; thus, *' some well-water is not 
fit to drink " is a particular negative proposition. 
Universal propositions also may be either negative or 
affirmative, so that as twice two make four, there come 
to be four principal kinds of propositions, namely, 
universal affirmative propositions, universal negative 
propositions, particular affirmative propositions, and 
particular negative propositions. We must go on to 
inquire more exactly into the nature and meaning of 
each of these four kinds of propositions. 

55. When we intend to make a statement about all 
the things which can be included under a term, we 
are said to take the term universally, or as logicians 
often say, the term is distributed. In the propo- 
sition "all coins are made of metal," the term "coins," 
as already explained, is taken universally, or is distri- 
buted, because the Httle adjective "all " indicates that 
the statement applies to any and every coin. But 
the predicate is only taken particularly and 
is not distributed ; it would be absurd to suppose 
that we intended to state that all things made of 
metal are coins. We can only have meant that all 
coins are among things made of metal, or are a part 
of them, and there exists, of course, an almost number- 
less variety of other things made of metal. We must 
carefully remember then that a universal affir- 
mative proposition like the one we have been 
examining, distributes its subject, but does not 
distribute its predicate. 

56. We may show very clearly the exact meaning 
of a proposition by imagining that the things we are 
speaking of are included in circles, like sheep in 
sheep-pens. Imagine that all things made of metal 
and only such are put in the larger circle in Fig. i, 
and all coins in the smaller circle. As the smaller 



/HI.] PROPOSITIONS. 43 

circle lies within the larger one, it follows that all coins 
are included among things made of metal, there being 




Fig. I. 

nothing but such inside the larger circle. We shall 
often find it convenient to use circles to show how one 
class or term is included wholly or partly in another, 
or excluded from it, as the case may be. 

57. As a universal negative proposition, let us take 
" No sea-weed is a flowering plant,'' and inquire care- 
fully what this means. It evidently speaks of all 
sea- weeds, so that the subject is distributed ; but does 
it take the predicate, flowering plant, in a universal 
sense? Our answer should depend upon whether or 
not we must examine all flowering plants before we 
decide that no sea-weed is a flowering plant. But, if 
we omitted to consider a single flowering plant, and 
this proved to be a sea-weed, our proposition would 
be untrue. The proposition asserts, then, that no 
sea-weed is the same as any flowering plant, so that 
there is complete separation between the two classes, 
and no object can be placed in both classes. 

58. We may show this in Fig. 2, the circle sup- 
posed to contain all sea-weeds lying quite outside 
of the circle containing all flowering plants. 

If any part of one circle were to lie over part of 
the other, some objects would be in both classes, 



44 PRIMER OF LOGIC, [viii. 

whereas the proposition asserts that no sea-weed is 
in any part of the class flowering plant. We arrive, 




Fig. 2. 

then, at this important truth, which should be carefully 
borne in mind, that the universal negative pro- 
position distributes, or takes universally, 
both its subject and its predicate. 

59. We shall have no difficulty in seeing that a 
particular affirmative proposition distributes 
neither its subject nor its predicate. Take 
as an example, "some violets are odorous." The 
subject " violets " is, of course, undistributed, because 
the proposition is particular. The predicate, moreover, 
is undistributed \ for it cannot be supposed that we 
intended to say that some violets are the only odorous 
things. There are a multitude of other flowers, and 
many substances which are odorous in addition to 
violets, so that the proposition must be taken as 
•^ some violets are some odorous things," or a part 
of odorous things. The predicate, then, as well as 
the subject, is taken particularly, or is undistributed. 

As other examples of the same kind of proposition 
I might mention the following : — many foolish novels 
are published ; most tunes in a minor key are melan- 
choly ; a few specimens of Saxon architecture still 
exist ; threepenny pieces are sometimes mistaken for 
fourpenny pieces. 



VIII.] PROPOSITlOm. 4S 

60. Coming, lastly, to a particular negative pro- 
position, say '^ some violets are not odorous," we 
know that the subject is undistributed, but we 
may easily discover that the predicate is 
distributed. Unless the some violets, of which we 
are speaking, were quite shut out of the class of 
odorous things, it would be untrue that they were 
inodorous. Hence we really mean that " some violets 
are not any odorous things," so that the predicate 
^* odorous things " is taken universally. 

61. When we try to show the meaning of particular 
propositions by using circles, it is difficult to avoid 
mistakes \ but we often make mistakes of the same 
kind in thinking and talking, and it is well to be 
aware of the fact. When we say '^ some violets arc 
odorous," we should generally be supposed to mean 
that ^' some violets " are so, and others are not ; but 
in this case one affirmative proposition really means 
the same as an affirmative one and a negative one 
put together, namely : — 

Some violets are odorous ; 
Some violets are not odorous. 

But it IS not logical to say one thing and mean 
another. When we say " some violets are odorous," 
we ought to be understood as meaning simply that 
" some are,'' leaving it quite uncertain whether other 
violets are or are not. In many cases we really 
should not know. I may safely say, for instance, that 
"some dogs are descended from wolves," it being 
nearly certain that some dogs are so ; but it may 
be afterwards ascertained that all dogs are so des- 
cended, or, on the contrary, that some are not so. 
I may say again that " some metals are combustible," 
without meaning to say that some are not. I may 
correctly say that " some men or most men laugh," 
without staying to inquire carefully whether all men 



46 



PRIMER OF LOGIC, 



[viii. 



do as a fact laugh. Not being sure that some men 
do not laugh, I must not be supposed to assert this, 
in saying that some do. In the absence then of any 
knowledge to the contrary, the word some must 
be taken to mean '' some and it may be all.*' 
I may safely say ^^some, and it may be all, dogs 
are descended from wolves," though it may afterwards 
be shown to be untrue that all dogs are so descended. 
62. Returning to the use of circles to show the 
meaning of the propositions in question we meet a 
similar difficulty. If I draw two circles crossing each 
other as in Fig. 3, and fill one circle with violets and 




Fig. 3. 

the other with odorous things, the figure evidently 
means that part of the class violets is in the class 




Fig. 



odorous things ; but then another part of the same 
class violets is outside the odorous things, so that 



IX. J P/^ POSITIONS. 47 

both the particular affirmative and the particular 
negative are shown at the same time. To avoid the 
difficulty we might perhaps use a circle with a part 
of its circumference broken. Thus, Fig. 4 would 
show that there certainly existed some violets inside 
the circle of odorous thmgs, but the broken line 
might be understood to mean that it was doubtful 
whether or not any violets were really outside the 
odorous things. Such a figure then indicates the 
meaning of the particular affirmative proposition. If 
the broken part of one circle lies inside the other 
circle, as in Fig. 5, the meaning will evidently be that 




Fig 5. 

some violets are known to be outside the odorous 
things, but that it is doubtful whether some violets 
are inside or not. This is the true meaning of the 
particular negative proposition. 

IX.— HOW TO CHANGE PROPOSITIONS. 

63. Having now carefully learned the nature of 
each of the four chief kinds of propositions, we must 
consider various ways in which we can draw or infer 
one proposition from another. We can often put the 
same truth into different words, just as we can mould 
the same clay into different forms, though it always 
remains the same clay. We can do likewise with 



48 PRIMER OF LOGIC. [ix. 

propositions ; it comes to the same thing, for instance, 
whether I say " all coins are metallic," or ^^ no coins 
are not metallic ; " or again '' there are no coins which 
are not metallic/^ 




Fig. 6. 

64. If, using circles again (see Fig. 6), we sup- 
pose all metallic things to fill up the larger circle, it 
follows that everything which is not metallic is outside 
the circle ; and, as all coins are supposed to be 
within the smaller circle, included in the greater one, 
it follows that none of the coins can be outside the 
greater circle, or among non-metallic things. It is 
evidently the same in the end to say that all coins 
are within the circle of metallic things, and that none 
of them are outside. In this way we can always 
change a universal affirmative proposition into a 
universal negative one of the same meaning, and we 
can make the change backwards again. Thus, to say 
^^ there are no things which may not be useful," is 
only a longer way of saying, ^^ all things may be 
useful." It is very desirable that the reader should 
practise himself in quickly and correctly making this 
and several other changes of propositions which I 
shall describe. 

65. We can always change a proposition by turning 
it about, so as to make the old subject into a ne\f 



IX. J PROPOSITIONS. 49 

predicate, and the old predicate into a new subject. 
We are then said to convert the proposition, 
and the new proposition is called the converse of 
the old one. But it does not follow that the new one 
will always be true if the old one was true. Some- 
times this is the case, and sometimes it is not. If 
I say, '* some churches are wooden buildings," I riiay 
turn it about and get, *' some wooden buildings are 
churches ; " the meaning is exactly the same as before. 
This kind of change is called simple conversion, 
because we need do nothing but simply change the 
subjects and predicates in order to infer a new pro- 
position. We see that the particular affirmative 
proposition can be simply converted. Such 
is the case also with the universal negative proposition. 
" No large flowers are green things " may be converted 
simply into "no green things are large flowers," by 
merely writing, " green things " in place of " large 
flowers," and large flowers instead of " green things." 




Fig. 7. 

Using circles (see Fig. 7), since the green things are 
quite separated from the large flowers, it evidently 
follows that the large flowers are quite separated from 
the green things. 

66. It is a more troublesome matter, however, to 
convert a universal affirmative proposition. The 
statement that "all jelly fish are animals," is true; 



so PRIMER OF LOGIC. [ix. 

but, if we simply convert it, getting *^ all animals are 
jelly fish," the result is absurd. This is because, as 
we learned before (Art. 55), the predicate of a uni- 
versal affirmative proposition is really particular. We 
do not mean to say that jelly fish are "all" the 
animals which exist, but only "some" of the animals. 
The proposition ought really to be, " all jelly fish are 
some animals," and if we converted this simply, we 
should get, " some animals are all jelly fish." But , we 
almost always leave out the little adjectives some and 
all when they would occur in the predicate, so that 
the proposition, when converted, becomes " some 
animals are jelly fish." This kind of change is called 
limited conversion, and we see that a universal 
affirmative proposition when so converted 
gives a particular affirmative one. 

67. This may seem all very plain and evident when 
we think about it carefully, yet it is very common to 
meet with people who fall into mistakes by hasty 
and careless thinking. By frequently seeing animals, 
we learn that they are all capable of moving them- 
selves in some way, and we get so accustomed to 
think " all animals are moving things," that, whenever 
we see a thing moving of its own accord, we are 
inclined to infer that it is an animal. We convert the 
proposition wrongly, and infer that "all moving things 
are anin)als." This is quite untrue ; for not only are 
there sensitive plants, fly-catchers, sun-dews, and some 
other large plants, which move almost like animals, 
but there is an immense number of very small plants, 
visible only in a good microscope, which continually 
move about quite as quickly as small animals. It is 
a curious fact, too, that very small particles of clay, 
mud, glass, or sand, when put into pure rain water, 
and examined by a strong microscope, are found to 
skip about as quickly as insects. 

(s^^. It is not unnatural, however, that people should 



IX.] PROPOSITIONS. 51 

sometimes make mistakes in converting propositions 
of the universal affirmative kind, because in not a few 
cases we can properly convert them simply. This 
is certainly the case when the subject and predicate 
are singular terms (Art. 14). Thus, "The Prince of 
Wales is the Duke of Cornwall,' and we may of 
course convert this simply into " The Duke of Corn- 
wall is the Prince of Wales." The poet Pope says, 
" The proper study of mankind is man ; " but we 
express exactly the same meanmg if we say, "man 
is the proper study of mankind." 

69. In other cases general terms may exactly co- 
incide one with another. It is a truth easily proved in 
geometry that all triangles with three equal sides have 
three equal angles; at the same time, all triangles 
with three equal angles have three equal sides. So 
that we might express the two truths at once, by 
saying, "all triangles with three equal sides are all 
triangles with three equal angles." This would be 
converted simply into " all triangles with three equal 
angles are all triangles with three equal sides." 
Whenever we meet, then, a proposition stating that 
one thing or class "is" another, or agrees with 
another, we ought to take the trouble to ascertain 
exactly whether the subject agrees with or makes the 
whole of the predicate or only part of it. In "all 
jelly fish are animals," of course the jelly fish are 
a small part only of the animals \ but the triangles 
with three equal sides exactly agree with the triangles 
with three equal angles, and there are no other 
triangles with three equal angles except those which 
have three equal sides. 

If we want to put one of the propositions which 
we hav^ just been considering into the form of a 
circulai diagram, a single circle will suffice. The 
circle containing "man" ought exactly to cover and 
coincide with that of the ^* proper study of mankind," 



52 



PRIMER OF LOGIC. 



[IX. 



if the poet Pope be correct. This is shown in 
Fig. 8. 




Fig. 8. 

70. There is yet another and a rather more difficult 
way of converting universal affirmative propositions. 
If '^all coins are metallic," it follows that '^all not- 
metallic things are not coins ; " but some people 
appear to be unable to see at first sight that this 
follows. A diagram, however, will make it plain. 
In Fig. 9, all metallic things are supposed to be inside 




Fig. 9. 



the larger circle, and all not-metallic things outside 
this circle. Now, as all coins are within the smaller 
circle, it is evident that none of the not-metallic 
things, which are outside the larger circle can be 



X.] SYLLOGISM. 53 

inside the smaller circle. Or, we may explain it in 
this way : — If all coins are metallic, it is impossible 
that what is not-metallic should be a coin, for then 
it would be also metallic, or the same thing would 
be at the same time not-metallic and metallic, which 
is absurd. From every universal affirmative pro- 
position we may then infer a new proposition, which 
has the negative of the former predicate as its subject, 
and the negative of the former subject as its pre- 
dicate. 

We can also make the same change backwards ; 
from " all not useful beings are not living beings," 
we can infer, '' all living beings are useful beings." 
For if we proceed to convert this last proposition in 
the way described, we get, " all not useful beings are 
not living beings," which is the proposition with 
which we began. 

X.-~SYLLOGISM. 

71. In a great many of the arguments which we 
most commonly use, one proposition is gathered or 
inferred from two other propositions. It is well 
known, for instance, that, ^^all Enghsh silver coins are 
coined at Tower Hill," and it is also known that, "all 
sixpences are Enghsh silver coins." It follows that 
*^all sixpences are coined at Tower Hill." These 
propositions are of the kind called universal affirmative, 
but we may give different names to them nevertheless, 
according to the place they hold in the reasoning. 
That last proposition which we gathered from the 
first two is called the Conclusion, probably because 
the argument is finished when we have learnt what it 
should be. The other two propositions, from which 
we gather or infer the conclusion, are called pre- 
mises, because they are put forward, or put first, for 
the purpose of being reasoned about. 



54 PRIMER OF LOGIC, [x. 

72. There will be no difficulty in seeing why the 
conclusion follows from the premises in the case 
given. For one premise tells us that *'all English 
silver coins are among those coined at Tower Hill/' 
though they are not the whole, as gold and bronze 
coins are also made there. The other premise informs 
us that "' all sixpences are among English silver coins," 
sixpences being again a part only of such silver coins. 
If we take three circles to con tarn respectively six- 
pences, English silver coins, and things coined at 
Tower Hill, as in Fig. ro, we see that sixpences are 




Fig. 10. 

among the things coined at Tower Hill, because they 
are among the English silver coins, which are coined 
there. 

73. As a second example of an argument in which 
we draw one proposition from two others, we will take 
the following: — 

All electors pay rates ; 
No paupers pay rates ; 

Therefore, no paupers are electors. 

Here the conclusion is a universal negative one, 
and it is inferred from two premises, the first of 
which is a universal affirmative, and the second a 



X.] SYLLOGISM, 55 

universal negative proposition. We may explain the 
reasoning in this way : all electors are among those 
who pay rates, whereas paupers are not among those 
who pay rates ; therefore the paupers are quite 
separated from the electors. Making use of circles 
again, we see that the circle of electors is inside that 
of those who pay rates, whereas the circle of paupers 
is outside, so that no part of the paupers' circle can 
touch or overlap that of electors. 

74. Although in these, and in some other cases, 
it is very easy to see that the conclusion will follow 



PAYING \ ^ — .. 



POOR-RATES 

(electors\ 



"kJ 



Fig. II. 



from the premises, this is not always the case. We 
must therefore examine how good syllogisms are made 
up, and what rules we must obey in making them. 
We will take again for this purpose our former ex- 
ample : — 

All English silver coins are coined at Tower Hill ; 
All sixpences are English silver coins ; 

Therefore all sixpences are coined at Tower Hill. 

We may observe that there are only three terms or 
classes of things reasoned about, namely, sixpences, 
English silver coins, and things coined at Tower Hill. 
Of these, the class of English silver coins does not 
occur in the conclusion ; it is only used to enable 



56 PRIMER OF LOGIC, [xi. 

US to compare or join together the other two classes 
of things, and in the diagram (Fig. lo, Art. 72) its 
circle lies between the other two circles. Accordingly, 
it is named the middle term. The largest circle 
is that containing all things coined at Tower Hill, the 
predicate of the conclusion, and this is called the 
major term of the syllogism, that is the larger 
term. Sixpences, on the contrary, being in the 
smallest circle, form the minor or the lesser 
term, which is always the subject of the conclusion. 

75. We shall have a great deal to do with major 
and minor and middle terms, and therefore I must 
ask the learner to remember carefully that the 
middle term is always the term which is not 
in the conclusion ; that the major term is 
the predicate of the conclusion ; and that 
the minor term is the subject of the con- 
clusion. It is also convenient to give separate 
names to the two premises, and that which contains 
the major term is always called the major premise, 
and that which contains the minor term, the minor 
premise. It is thought to be more correct to write 
the major premise first, but even if it be put second 
it is still called the major premise because it con- 
tains the major term. 



XI.— THE RULES OF THE SYLLOGISM. 

76. To find out whether an argument which seems 
to be a syllogism is really a syllogism, we must 
examine it carefully, and ascertain whether it agrees 
with certain rules. The great logician Aristotle more 
than two thousand years ago discovered these rules 
and showed how to decide when supposed syllogisms 
are good, and when they are not good. Several 
logicians have in the last fifty years been trying to 



XL] SYLLOGISM. 57 

find out some simpler and better mode of ascertaining 
when arguments are good, but they have not yet 
agreed upon the subject. Until they do agree upon 
something better, we shall do well to learn the old 
rul'es, which are certainly both ingenious and useful. 

77. Rule I, — In the first place a syllogism must 
contain three terms, and not more than three 
terms ; for the reasoning consists in comparing two 
terms with each other by means of a third term, 
which we have called the middle term. If, then, 
there were four terms, the argument would consist 
either of two syllogisms, or of none at all. Suppose 
the terms to be cow, cloven-footed animal, ruminating 
animal, and animal having two stomachs. I may say 
that "all cows are cloven-footed animals," and that 
" all ruminating animals have two stomachs ; " but 
this will not give the conclusion " all cows have two 
stomachs," unless we have yet another proposition 
comparing cloven-footed animals with ruminating 
animals. But, with this third proposition, we can 
make two complete syllogisms, the first proving that 
cows are ruminating animals, because they are cloven- 
footed, and all cloven-footed animals are ruminating 
animals ; and the second in like manner showing that 
because cows are ruminating animals, therefore they 
have two stomachs. 

A syllogism then must have just three terms, 
neither more nor less, and these terms are called, as 
we have already learned (Art. 74), the major, middle, 
and minor terms. 

78. Rule II. — A syllogism must consist of 
three propositions, and only three proposi- 
tions, of which one is the conclusion, and the other 
two are the major and minor premises. For if there 
be four propositions, one will be the conclusion and 
the other three premises. But two premises are 
sufficient to compare two terms with a middle term, 



58 PRIMER OF LOGIC, [XL 

SO that three premises will either make no such 
comparison at all, or will make two syllogisms. We 
may easily see this by considering again the case of 
cows. Two propositions enable us to show that a 
cow is a ruminating animal, because it is cloven- 
footed ; and a third proposition enables us to make 
a new syllogism showing that it also has two 
stomachs. 

79. Rule II L — It is an important rule that the 
middle term of a syllogism must be distri- 
buted, that is, taken universally, or in its 
whole extent of meaning, once at least in the 
premises. The reason for this rule is not quite so 
easy to explain, but it will afterwards be made pretty 
evident by examples. It amounts to this, that unless 
we take the whole of the middle term once, the two 
premises may refer to different parts of the middle 
term, so that there may really be no true middle term 
at all. If I say that " some animals are flesh-eating 
animals," and "" some animals have two stomachs," 
it would be absurd to infer that therefore flesh-eating 
animals have two stomachs. The " some animals " 
which are flesh-eating, may be, and in fact are, quite 
distinct from the other '^ some animals " which have 
two stomachs. We may in fact say that there are 
four terms, and that we thus break the first rule of 
the syllogism, although there seem to be only three 
terms. But if I argue that, because " some animals 
are flesh-eating," and ** all animals consume oxygen," 
therefore " some animals consuming oxygen are flesh- 
eating," there must be a good middle term. The 
"some animals" in the major premise must be part 
of the ^' all animals " in the minor premise, and thus 
we have a sure means of comparison between the 
major and minor terms. 

80. Rule IV. — This rule is to the eflect that we 
must not infer anything about the whole of a term, 



XI.] SYLLOGISM, 59 

unless something was said about the whole of the 
term in the premises. In other words, no term 
must be distributed in the conclusion unless 
it was distributed in the premises. It would 
be absurd to argue that because brittle substances are 
not fit for coining, and some metals are brittle sub- 
stances, therefore no metals are fit for coining. We 
can, of course, infer that ^* some metals " are not fit 
for coining, namely, those which are brittle ; but to 
include other metals as well is simply to suppose we 
have knowledge about them which is not given in the 
premises at all. It is not always so easy to find out 
when this rule is broken. To go back to the example 
in Art. 79, because some animals eat flesh, and all 
animals consume oxygen, we must not conclude that 
all which consume oxygen eat flesh. We must re- 
member that the minor premise, " all animals consume 
oxygen," is an affirmative proposition, which, as fully 
explained in Art. 55, does not distribute its predicate, 
that is, does not refer to all things which consume 
oxygen. In other cases the way in which this fourth 
rule is broken will be still less apparent at first sight, 




Fig. 



but these cases will be described further on (Art. 87 
88). 



6o PRIMER OF LOGIC. [xi. 

8 1. Rule V. — It is very certain that from two 
negative premises nothing can be inferred. 

A negative proposition asserts that two terms differ, 
so that the classes of things denoted by the terms are 
wholly or partly separated from each other. If we 
say then that no Englishmen are slaves, and that 
no negroes are Englishmen, we must represent the 
Englishmen by a circle quite separate from that of 
the slaves, and the negroes by a circle quite separate 
from that of Englishmen. But then we shall see after 
very little consideration that the negroes' circle may 
be placed either quite away from that of the slaves, 
or may be made to overlap it more or less. This 
means that negroes may be not slaves at all, or may 
be partly slaves and partly not slaves, or may be 
all slaves, for anything which the two premises tell 
us about the matter. 

82. Rule VL — The last of the principal rules of 
the syllogism is that, if one premise be negative, 
the conclusion must be negative, and we 
cannot get a negative conclusion unless one 
of the premises be negative. We may perhaps 
see the truth of this rule most easily by reflecting that 
a negative proposition is represented by one circle 





Fig. 13. 



outside nnother. Now, if we say all negroes are dark, 
no Englishmen are dark, the circle of negroes is 
inside that of dark men, while that of Englishmen is 



XI.] SYLLOGISM. 6i 

outside, so that the circle of Englishmen must be 
outside that of negroes, giving a negative result. It 
is true that we might have the terms differently 
arranged. The premises might be all negroes are 
dark, no Chinese are negroes. The circle of negroes 



(I CHIN-\ 



Fig. 14. 

is as before inside that of dark men ; but the circle 
of Chinese, though outside that of negroes, may be 
wholly inside that of dark men, or partly inside and 
partly outside, or wholly outside. Such premises then 
tell us nothing about the relative position of Chinese 
and negroes, and we see that with one negative 
premise we either get a negative conclusion, or no 
conclusion at all. 

83. A second part of the rule is that we cannot 
get a negative conclusion unless one premise be 
negative. We may satisfy ourselves that this is true 
by trying with circles how we can prove one circle 
to be outside of another by means of a third circle. 
This can only be done by putting one inside and one 
outside the third circle, and to put one outside 
another indicates, as we have often seen, a negative 
proposition. 

84. Everyone who wishes to be a good logician 
must remember the rules of the syllogism which have 
now been described, and must by practice become 



62 PRIMER OF LOGIC. [xi. 

quick in seeing whether an argument supposed to be 
a syllogism does or does not obey the rules. I will 
give a few more examples of the way in which we 
must examine arguments in order to decide whether 
they are good syllogisms or not. Do the following 
premises, for instance, allow of the conclusion drawn 
from them? — 

Every city contains a cathedral. 
Liverpool does not contain a cathedral. 
Therefore, Liverpool is not a city. 

Here the middle term, or that which does not 
appear in the conclusion, is " contain (or containing) a 
cathedral." The minor term is Liverpool, and the 
major term city. There are thus three terms and no 
more, in accordance with the first rule, and there are 
three propositions and no more, in accordance with 
the second rule. The third rule requires that the 
middle term shall be distributed, or taken universally, 
once at least; and this is the case, because the 
second premise " Liverpool does not contain a cathe- 
dral^' is a negative proposition, and therefore dis- 
tributes its predicate (Art. 57). As to the fourth rule, 
Liverpool and city are both distributed in the con- 
clusion, but they are also both distributed in the 
premises, so that the rule is obeyed. The first pre- 
mise is affirmative, so that the fifth rule about two 
negative premises cannot be broken. The sixth rule 
is likewise obeyed, which requires that if one premise 
be negative the conclusion shall be so, and this is the 
case. Thus, the argument we are discussing is a 
perfectly good syllogism. 

85. Let us next examine whether the following pro 
positions make a syllogism : — 

All mmerals are raised from mines. 
All coals are raised from mines. 
Therefore, all coals are minerals. 



XI.] SYLLOGISM. 



The middle term, which we should generally look 
for 6rst, is " raised from mines ; " but we ought to 
notice at once that both the propositions in which it 
appears are affirmative. Now" affirmative propositions 
never distribute their predicates (Arts. 55, 59), so that 
the third rule of the syllogism is broken, which re- 
quires that the middle term shall be distributed once 
at least. In this case there is said to be a fallacy 
of an undistributed middle term. 

"^(i. This was the kind of fallacy into which an 
authoress fell when she wrote a book proving, among 
other things, that to wear false hair was to tell a false- 
hood. In reality her reasoning came to this, that to 
wear false hair was to deceive, and to tell a falsehood 
was also to deceive. But the predicate to deceive is 
in both cases particular and ought to be explained as 
meaning one way of deceiving. Now falsehood is 
the name for deceit by words, and is not the proper 
name for deceit by other means. 

To make a good argument out of this matter we 
ought to be able to put it in this way ; — 

To deceive is always to tell a falsehood. 
To wear false hair is to deceive. 

Therefore, to wear false hair is to tell a falsehood. 

This is a perfectly good syllogism supposing it 
to mean that every case of deceiving is a case of 
telling a falsehood, and if this were true the conclusion 
would be true. But it is evident that in the ordinary 
use of the word falsehood the first premise is not true. 
There was one philosopher who tried to prove in like 
manner that whenever a person did a wrong act it 
was onlv a particular way of telling a lie, so that one 
who killed a fellow-creature only took a round-about 
way of saying that he was not a fellow-creature. 

87. It is not unnatural that people, who spend their 



64 PRIMER OF LOGIC. [xi. 



whole lives in some kind of study, should learn to 
perceive all its value, while, being ignorant of other 
branches of learning, they cannot so readily know the 
value of those branches. Hence they are likely to 
fall into the fallacy of arguing that because their own 
studies are very useful other studies are not. Let 
us take the study of Latin and Greek as an instance, 
and compare it with that of physical science. The 
argument would be put in this form : — 

The study of Greek and Latin is very useful ; 
The study of physical science is not the study of 
Greek and Latin ; 

Therefore, the study of physical science is not very 
useful. 

In this argument the numbers of terms and pro- 
positions are quite correct, and at the first moment 
it may not be easy to see where it fails. The middle 
term, or that which does not appear in the conclusion, 
is "the study of Greek and Latin." It is certainly 
distributed in the second premise which is negative, 
and may also be said to be distributed in the first 
premise, being in fact a singular term. One premise 
is negative and the conclusion is negative. So far 
all is right ; but on making further examination, we 
shall find that the conclusion, being negative, dis- 
tributes its predicate "very useful," while the first 
premise, of which it is also the predicate, does not 
distribute it. Thus the supposed argument breaks 
the fourth rule, that no term shall be distributed in 
the conclusion unless it were distributed in one of the 
premises, 

88. The fact is, of course, that there may be a 
great many very useful studies, and because the 
classical studies of Greek and Latin are some of these, 
it does not follow that other ones are shut out. We 
may show this most clearly by a diagram (Fig. 15), 



XL] 



n'LLOGISM. 



65 



placing the several studies in smaller circles enclosed 
in the larger one of very useful studies. The circle 




Fig. 15. 



of Greek and Latin must be distinct from that of 
physical science, and these circles must not over- 
lap each other at all ; but we see that the circle of 
physical science may nevertheless be placed so as to 
be wholly within that of " very useful studies," or partly 
within and partly without, or wholly without. In short, 
from the statement that Greek and Latin are very 
useful subjects of study, we get no information at 
all as to whether the physical sciences are or are not 
so. We may say the same of the study of mathe- 
matical, logical, moral, and other sciences. None 
of them must be considered useless, because the 
others are useful. 

89. Suppose I were to argue that all householders 
pay poor rates, and all electors are those who pay 
poor rates ; therefore, all householders are electors. 
Now, as a matter of fact, it is true according to the 
present law that all householders, excepting paupers, 
are electors; but does this follow from the pro- 
positions used as premises to reason upon? The 
middle term seems to be " paying poor rates,'' and 



66 PRIMER OF LOGIC, [xi. 

it is the predicate of both the premises, which are 
afifirmative. 1 herefore it would in each case be 
undistributed, and by the third rule of the syllogism, 
the argument would be bad. But great care is often 
required in examining arguments, and in reality the 
second proposition is not what we took it to be. We 
do not simply say, " all electors pay poor rates,'^ or 
are "" among those who pay poor rates ;'^ but we say 
that they " are " those, so that there are no electors 
(in ordinary cases) except those who pay poor rates. 
This is one of those propositions (Art. 68) which we 
can convert simply, so that we may state it as, ^^all 
who pay poor rates are (all) electors ; " and as all 
householders pay poor rates, excepting paupers, it 
follows by a good syllogism, that all householders are 
electors. 

90. There are two minor rules of the syllogism 
which we may deduce from the rules already given. 
The first is that from two particular propositions, 
whether affirmative or negative, we cannot deduce any 
logical conclusion. Thus, if we were to argue that 
some who elect members of Parliament are well- 
educated men, and some well-educated men are per- 
fectly acquainted with what the country needs, we 
could not properly infer that some who elect members 
of Parliament are perfectly acquainted with what the 
country needs. The middle term is " well-educated 
men," and it is the predicate of the first of the pro- 
positions, so that it is undistributed. It is also 
undistributed as the subject of the second proposition, 
and thus what seems to be an argument breaks the 
third rule of the syllogism. As we may explain it, 
the well-educated men who elect members of Parlia- 
ment might happen not to be those perfectly ac- 
quainted with what the country needs. In the same 
way, if we were to take other examples of arguments 
containing two particular propositions, we should find 



XI.] SYLLOGISM. 67 

that they can never give a conclusion according to 
the rules of the syllogism. 

91. A second rule which follows from those of the 
syllogism is that, if either premise be particular, the 
conclusion must also be particular. If we were to 
argue that some electors are not fit to choose good 
representatives, but all well-educated men are fit 
to choose good representatives, therefore no electors 
are well-educated men, we should break the fourth 
rule of the syllogism. We must not infer anything 
at all about all electors, when in the first proposition 
we speak only of some electors. In a similar way 
every syllogism in which one premise is particular and 
the conclusion is not particular will be found to break 
one rule or other of those given in Arts. 77 — 82. 

92. It is shown in almost all books on logic that, 
when we try in how many difi'erent w^ays we can make 
syllogisms with each of the four kinds of propositions 
variously put together, we get altogether nineteen 
good kinds of arguments, called the nineteen 
moods of the syllogism. These are divided into 
four figures, each figure being known by the position 
of the middle term in the premises. Logicians long 
ago ascertained in what cases of each figure a syl- 
logism is valid, and they recorded the results in 
certain curious lines, beginning Barbara, Celarent, &c., 
which were so constructed that the vowels in each 
word show what kinds of propositions put together 
in a particular way will make a good syllogism. But 
it is not of much advantage to know these lines by 
heart, because we ought to understand the rules of 
the syllogism so well as to be able to tell in every 
case whether an argument is a correct syllogism 
or not. 

93. Although every argument which is a good 
syllogism must consist of two premises and a con- 
clusion, these three propositions will not usually be 



6^ PRIMER OF LOGIC. [xi. 

Stated at full length. People sometimes think that 
they are not arguing by syllogisms, because the parts 
of the syllogisms are not written or printed exactly 
as they are in books on logic. But they might as 
reasonably say that mental arithmetic is not arithmetic 
at all, because the sums are not worked out at full 
length on paper. It is not usual to state more than 
one premise of a syllogism in addition to the con- 
clusion, because the reader can then judge, without 
much difficulty, what the other premise is intended 
to be. Thus in the Sermon on the Mount, the verses 
known as the Beatitudes consist each of one premise 
and a conclusion, and the conclusion is put first. 
" Blessed are the merciful : for they shall obtain 
mercy." The subject and predicate of the con- 
clusion are here inverted (Art. 69), so that the pro- 
position is really " The merciful are blessed." It is 
evidently understood that '' All who shall obtain mercy 
are blessed," so that the syllogism, when stated at 
full length, becomes : — 

All who shall obtain mercy are blessed ; 
All who are merciful shall obtain mercy; 

Therefore, all who are merciful are blessed. 

This is a perfectly good syllogism, similar to those 
described in Arts. 10 and 74. _ 

94. Wherever any one of the words, because, 
for, therefore, since, or other words used in the 
same sense occur, we may be sure that there is an 
argument, and in many cases this will be found to 
be a syllogism. It is true that a great many of 
the arguments which we commonly use belong rather 
to geometrical or arithmetical reasoning, than to 
simple logic. If I were to argue, for instance, that 
the rocks called red sandstone lie above the coal 
measures, because they lie above the Permian rocks, 
which lie above the coal measures, this is perfectly 



XII.] HYPOTHETICAL SYLLOGISMS. 69 

good reasoning. But it is not merely logical, because 
it deals with the position of the beds of rocks. It 
is a question of height, and belongs to geometry. 

XII.-HYPOTHETICAL SYLLOGISMSo 

95. It was stated (Art. 51) that there are supposed 
to be three kinds of propositions, of which the first 
and most common kind is employed in the syllogisms 
already described. We must not overlook hypo- 
thetical propositions which affirm something pro- 
vided or *' if" something else is true. By joining one 
such proposition with an ordinary proposition we can 
make a syllogism. " If Manchester contains a cathe^ 
dral it is a city; but Manchester does contain a 
cathedral ; therefore, it is a city," This is an affirmative 
hypothetical syllogism, and it has two premises and a 
conclusion, Uke an ordinary syllogism. The first pre- 
mise is hypothetical and consists of two parts, the 
antecedent containing the little word "if,'' and the 
consequent which informs us what will happen undei 
the supposed circumstances. 

96. The rules of this kind of syllogism are very 
simple : If the antecedent be affirmed, the 
consequent may be affirmed. If the conse- 
quent be denied, the antecedent may be 
denied. In the instance already given the first rule 
applies ; for we affirm that Manchester does contain a 
cathedral, and then affirm the consequence, that it is 
a city. As an example of the second rule, we may 
say, " If the atmosphere were equally dense at all 
heights there could be no perpetual snow on the Alps ; 
but there is perpetual snow on the Alps : therefore, the 
atmosphere is not equally dense." This is a negative 
hypothetical syllogism. 

97. We must take much care not to fall into 
the fallacies of affirming the consequent, or 



70 PRIMER OF LOGIC, [xil 

denying the antecedent, and imagining that we 
are making a good syllogism. It would be wrong to 
argue that, " If a man is a good teacher, he thoroughly 
understands his subject ; but John Jones thoroughly un- 
derstands his subject; therefore, he is a good teacher." 
The conclusion may happen to be true, as a matter of 
fact, but it does not follow from the premises. Nor 
can we argue that, " If snow is mixed with salt it 
melts ; the snow on the ground is not mixed with 
salt ; therefore it does not melt." This argument is 
obviously absurd, because snow melts when warmed, 
as well as when mixed with salt, and by denying the 
one possible antecedent we leave other possible ones 
untouched. 

98. In reality, however, hypothetical propositions 
and syllogisms are not different from those which we 
have more fully considered. It is all a matter of 
the convenience of stating the propositions. 
Thus, our forrfier example (Art. 95) may be stated 
thus: — '^ All towns containing cathedrals are cities; 
Manchester is a town containing a cathedral ; there- 
fore, Manchester is a city." This is a good syllogism 
of a very common kind, the middle term being ** town 
containing a cathedral." Our second example is not 
so conveniently stated as a common syllogism, but we 
may say, " An equally dense atmosphere is not an 
atmosphere allowing perpetual snow on the Alps; 
but our atmosphere is one allowing perpetual snow on 
the Alps : therefore, our atmosphere is not an equally 
dense atmosphere." This is a good syllogism with a 
negative major premise and a negative conclusion, 
and all the other hypothetical syllogisms can be turned 
into ordinary ones in the way shown by one example 
or the other. 

99. We can now see that to affirm the conse- 
quent and then to infer that we can affirm 
the antecedent, is as bad as breaking the 



XIII.] ARGUMENTS. 71 

third rule of the syllogism, and allowing an 
undistributed middle term. This is very evident in 
the example given (Art. 97) which becomes, ^' A good 
teacher thoroughly understands his subject ; John 
Jones thoroughly understands his subject ; therefore, 
John Jones is a good teacher. " Both the premises being 
affirmative and having the middle term "thoroughly 
understands his subject^'* for their predicate, it follows 
that the middle term is not distributed in either pre- 
mise. 

To deny the antecedent is really to break 
the fourth rule of the syllogism, and to take 
a term as distributed in the conclusion which was 
not so in the premise. Instead of saying, " If snow is 
mixed with salt it melts ^' we may say more simply, 
** Snow mixed with salt melts ; but the snow on the 
ground is not mixed with salt ; therefore, it does not 
melt.'' Here the conclusion is negative, and therefore 
distributes its predicate "melts" or "melting." But 
this term occurs as the predicate of the first premise, 
which is affirmative, so that it is not distributed, break- 
ing the fourth rule of the syllogism. This example is 
exactly like that given in Article 87. 

XIII.-OTHER KINDS OF ARGUMENTS. 

100. It would be quite a mistake to suppose that 
all good logical arguments must obey the rules of the 
syllogism, which we have been considering. Only 
those arguments which connect two terms together by 
means of a middle term, and are therefore syllogisms, 
need obey these rules. A great many of the arguments 
which we daily use are of this nature \ but there are 
a great many other kinds of arguments, some of which 
have never been understood by logicians until recent 
years. 

10 1. One important kind of argument is known as 



72 PRhMER OF LOGIC. [xiii. 



the disjunctive syllogism, though it does not obey 
the rules of the syllogism, or in any way resemble 
syllogisms. We learned (Art. 52) that disjunctive 
propositions are those which have several terms joinec! 
together by the Httle word " or." We use such pro 
positions when we divide up a class into smaller 
classes ; thus we may say, speaking without scientific 
accuracy, that a vegetable is either a tree, or a shrub, 
or a herb. A boat is either a saiUng-boat, or a row- 
boat, or a steam-boat. The metal of which money is 
made is either gold, or silver, or copper, or bronze, or 
nickel. There may be any number of things thus 
stated ; for instance, a member of the House of 
Commons must be either Mr. Disraeli, or Mr. Glad- 
stone, or Mr. Forster, or Sir Stafford Northcote, or 
any one of about 650 other men who belong to the 
House. Each of the things or smaller classes thus 
joined together by '' or" will be called alternatives, 
because we may take our choice between them, and 
if one will not do another may do. 

102. The principal rule according to which we use 
disjunctive propositions in arguments is that if one 
or more alternatives be denied the rest may 
be affirmed. Thus fuel consists of carbon or 
hydrogen. If then any particular portion of fuel 
does not consist of hydrogen, it must consist of carbon. 
Here there are only two alternatives, and in this and 
a great many like cases, if we deny one alternative we 
must affirm the only remaining one. A crime is either 
treason, or felony, or misdemeanour. Forgery is not 
treason nor misdemeanour; therefore, it is felony. 
Here we have three alternatives, two of which are 
denied, so that the other one alone remains to be 
affirmed. Roofing materials are either slates, or thatch, 
or shingles, or iron, or tiles, or felt, or paper. Here 
we have seven alternatives, and, if we held them to 
be all the existing ones, it would follow that a house 



5CIV.] RULE OF INFERENCE. ' 73 

not roofed with slates or thatch must be roofed with 
shingles, or iron, or tiles, or felt, or paper. These 
disjunctive arguments, it will be seen, may be very 
various in the number of alternatives denied and 
affirmed ; but they none of them obey the rules of the 
syllogism, because one proposition is always negative 
and yet the conclusion is affirmative, which is against 
the sixth rule (Art. 82). 

103. It is said in some books on logic that, if we 
affirm one alternative of a disjunctive proposidon, we 
must deny the remainder. It would be said, for 
instance, that as fuel is composed of carbon or of 
hydrogen, what fuel is composed of carbon is not 
composed of hydrogen. But this is not true, because 
nearly all fuel is composed of both substances at the 
same time. Again, it might be inferred that, as boats 
are either sailing-boats, or row-boats, or steam-boats, 
therefore a boat which is a steam boax is not a sailing- 
boat, nor a row-boat. But this need not be so, and 
most steam-boats are able to set sails, when it is 
desirable or necessary to do so. A magistrate is a 
justice of the peace, or a mayor, or a stipendiary 
magistrate ; but it does not follow that one who is a 
justice of the peace is not a mayor. After affirming 
one alternative we can only deny the others if there 
be such a difference between them that they could 
not be true at the same time. 

XIV.— THE GREAT RULE OF INFERENCE. 

104. There is a simple rule which will enable us tc 
test the truth of a great many arguments, even of 
nany which do not come under any of the rules com- 
monly given in books on logic. This rule is that 
whatever is true of one term is true of any 
term which is stated to be the same in mean- 
ing as that term. In other words, we may always 



74 PRIMER OF LOGIC, [xiv. 

substitute one term for another if we know 
that they refer to exactly the same things. 

There is no doubt that a horse is some animal, and there- 
fore the head of a horse is the head of some animal. 
This argument cannot be brought under the rules of 
the syllogism, because it contams four different logical 
terms in two propositions, namely, horse, some animal, 
head of horse, head of some animal. But it easily 
comes under the rule which I have given, because we 
have simply to put '' some animal " instead of ''' a 
horse.'' A very great number of arguments may be 
explained in this way. Gold is a metal ; therefore, a 
piece of gold is a piece of metal. A negro is a 
fellow creature ; therefore, he who strikes a negro, 
strikes a fellow creature. A domestic animal is a 
creature capable of suffering ; therefore, he who ill- 
treats a domestic animal, ill-treats a creature capable 
of suffering. 

105. Let it be carefully remarked that in an ordinary 
universal affirmative proposition, like, " A negro is a 
fellow creature," we cannot put negro simply for 
fellow creature. It would be absurd to argue that, 
because a man strikes a fellow creature, therefore he 
strikes a negro. This is evidently because negroes 
form only a part of our fellow creatures. But in other 
cases, as already mentioned (Art. 69), the subject and 
predicate of a proposition refer to exactly the same 
numbers of objects, and altogether coincide. All 
parallelograms, for instance, are all plane four-sided 
figures, whose opposite angles are equal. It follows 
that whatever we know of a four -sided figure of this 
description is true of a parallelogram, and whatever 
we know of parallelograms is true of such figures. 
Any figure which has not its opposite angles equal 
cannot be a parallelogram. When the terms of a 
proposition are singular ones, this is still more evident. 
The moon is the earth's satellite ; it follows that any- 



XIV. J RULE OF INFERENCE, 75 

thing which is true of the earth's satellite is true of 
the moon ; and anything which is true of the moon is 
true of the earth's satellite. The moon, as far as we 
can learn, is without an atmosphere, and without seas ; 
therefore the earth's satellite is without an atmosphere 
and without seas. 

106. It is really in the same way that we argue 
about quantities. Thus the length of Westminster 
Abbey is 505 feet ; therefore, anything true of 505 feet 
is true of the length of Westminster Abbey. The 
length of Canterbury Cathedral is greater than 505 
feet by 9 feet ; therefore it is greater than that of 
Westminster Abbey by 9 feet. The width of Bristol 
Cathedral is equal to that of Bath Abbey Church. 
Hence it follows that, in respect to widih, we can 
always put Bristol Cathedral for the Bath Abbey 
Church, or the latter for the former. It happens, for 
instance, that the width of St. Mary's Church, at 
RedcHffe, Bristol, is less than that of the Cathedral ; 
hence it follows that it is less than that of the Bath 
Abbey Church. On the otlrer hand, Exeter Cathedral 
has by accident the same width as Bristol Cathedral; 
therefore, putting the Bath Abbey Church for Bristol 
Cathedral, we find that the Cathedral of Exeter and 
the Bath Abbey Church have the same width. 

107.. When we examine carefully enough the way 
in which we reason, it will be found in every case 
to consist in putting one thing or term in 
place of another, to which we know it to 
have an exact resemblance in some respect. 
We use the likeness as a kind of bridge, which leads 
us from a knowledge of one thing to a knowledge 
of another; thus the true principle of reasoning 
may be called the substitution of similars, 
or the passing from like to like. We infer the 
character of one thing from the character of some- 
thing which acts as a go-between, or third term. 



76 PRIMER OF LOGIC. [xv. 

When we are certain there is an exact likeness, oui 
inference is certain ; when we only believe that there 
probably is, or guess that there is, then our inferences 
are only probable, not certain. 

XV.— INDUCTIVE REASONING. 

1 08. In all the preceding parts of this Primer we 
have been inquiring how we may gather the truth 
contained in some propositions, called Premises, and 
put it into another proposition, called the Conclusion. 
We have not yet undertaken t(? find out how we can 
learn what propositions really are true, but only 
what propositions are true when other ones 
are true. All the acts of reasoning yet considered 
wojld be called deductive, because we deduce, 
or lead down the truth from premises to con- 
clusion. It is an exceedingly important thing to 
understand deductive inference correctly, but it might 
seem to be still more important to understand induc- 
tive inference, by which we gather the truth of 
general propositions from facts observed as happening 
in the world around us. 

109. It ought to be easy to see that reasoning alone 
will never teach us anything, because it only gives us 
one proposition, when we already have other ones. 
How then are we to get the original propositions ? 
This must be done by using our eyes and ears, and 
observing things about us, so as to learn what they 
really are. How are we to know that all very small 
particles of w^ater in daylight appear white, except by 
examining the appearance of clouds, mist, foam, spray, 
steam, and any other things which we know to be 
composed of small particles of water? This seems 
to be evidently the proper way to get knowledge, and 
we may well wonder that people ever thought differ- 
ently. Nevertheless, for many centuries it was bellowed 



XVJ IJSrDUClIVE REASONING. 77 

to be possible to arrive at all necessary knowledge by 
the use of the syllogism, and men preferred trusting 
to Aristotle, rather than using their own eyes. 

no. The rise of modern science may perhaps be 
considered to date as far back as the time of Roger 
Bacon, the wonderful monk and philosopher of Oxford, 
who lived between the years 12 14 and 12920 He 
was probably the first in the middle ages to assert 
that we must learn science by observing and experi- 
menting on the things around us, and he himself 
made many remarkable discoveries. Galileo, however, 
who lived more than 300 years later (1564 to 1642), 
was the greatest of several great men, who in Italy, 
France, Germany, or England, began by degrees to 
show how many important truths could be discovered 
by well-directed observation. Before the time of 
Galileo, learned men beheved that large bodies fall 
more rapidly towards the earth than small ones, 
because Aristotle said so. But Gahleo, going to the 
top of the Leaning Tower of Pisa, let fall two un- 
equal stones, and proved to' some friends, whom he 
had brought there to see his experiment, that Aristotle 
was in error. It is Galileo's spirit of going 
direct to Nature, and verifying our opinions 
and theories by experiment, that has led to 
all the great discoveries of modern science. 

Tiio People very commonly believe that Francis 
Bacon, usually called Lord Bacon, who lived between 
the years 1561 and 1629, was the founder of inductive 
logic and of true scientific method. It is quite certain 
that Lord Bacon was an exceedingly clever man, and 
in many ways a great man. In his celebrated work, 
the Novum Organum, or the New Instrument, 
he strongly points out the need of observing Nature 
and collecting a great many facts, from which general 
laws might gradually be collected, and he foresaw that 
vahiable discoveries would be made. But it is quite a 



78 PRIMER OF LOGIC. [xv. 

mistake to suppose that Lord Bacon really understood 
the inductive logic by which Galileo, about the same 
time, and Sir Isaac Newton and other great men after 
him, succeeded in detecting the chief laws of nature. 
Not only was Lord Bacon unable to make any 
real discoveries by his own methods of inquiry, when 
he tried to do so, but he could not see the truth of 
the excellent discoveries in astronomy and magnetism, 
which Copernicus, and an EngUshman named Gilbert, 
had made known a little time before. Thus it is 
wrong to speak of Lord Bacon's philosophy as if his 
book the Novum Organu77i really taught men how to 
investigate nature, and if we continue to speak of 
Bacon's Philosophy, meaning the new inductive logic, 
we ought to attribute it to Roger Bacon 
rather than to Lord Bacon. 

112. Inductive logic inquires by what man- 
ner of reasoning we can gather the laws of 
nature from the facts and events observed. 
Such reasoning is called induction, or hiductive 
inquiry, and, as it has actually been practised by all 
the greatest discoverers in science, it consists in four 
steps. 

113. In the first place, we must gain, by almost 
accidental observations and experiments, a knowledge 
of facts touching the subject of inquiry. Such know- 
ledge of mere facts is not properly called science at 
all, because the facts are disconnected, and do not 
enable us to explain other facts, or to discover what 
will happen before v/e have tried the experiment. It 
is merely knowledge given by the senses. 

114. In taking the second step, we proceed to 
reason about these facts, which we do by inventing 
or imagining laws^ which may be true of the things 
examined. We make what is called an hypothesis 
and suppose some law or general proposition to be 
true for the sake of argument. We see now why 



XV.] INDUCTIVE REASONING. 79 

deductive logic is so very important, because it is 
only by deductive reasoning that we can tell what will 
be the consequences of the law or proposition sup- 
posed. 

115. In the third step, then, we reason by the 
syllogism, or by other kinds of deductive argument, 
to the particular facts which will be true if the hypo- 
thesis be true. 

116. In the fourth step, we proceed to compare 
these deductions with the facts already collected, or, 
when necessary and practicable, we make new observa- 
tions and ■ plan new experiments, so as to find out 
whether, the hypothesis agrees with nature. If we 
meet with several distinct disagreements between our 
deductions and our observations, it will become likely 
that the hypothesis is wrong, and we must then invent 
a new one. In order to produce agreement it will 
sometimes be enough to change the hypothesis in a 
small degree. 

117. When we get hold of an hypothesis which 
seems to give results agreeing with a few facts, we 
must not at once assume that it is certainly correct. 
We must go on making other deductions from it under 
various circumstances, and, whenever it is possible, we 
ought to verify these results, that is compare them 
with facts observed through the senses. When an 
hypothesis is shown in this way to be true in a great 
many of its results, especially when it enables us 
to predict what we should never otherwise have 
believed or discovered, it becomes almost certain that 
the hypothesis itself is a true one. 

118. Thus there may be said to be four different 
steps in inductive reasoning : — 

First Step. — Preliminary observation. 
Second Step, — The making of hypotheses. 
Third Step, — Deductive reasoning. 
Fourth 5/<^.— Verification. 



So FRIAIER OF LOGIC. [xv. 



I will now proceed to show by examples that it 
is really by this mode of reasoning in four successive 
steps that we learn the nature of things, and thus 
become able to make true general propositions about 
them. 

119. Hundreds of years ago people had frequently 
noticed in stones and on the face of exposed rocks, 
peculiar forms closely resembling those of living 
animals, shells, or plants. These fossils were so re- 
markable that, though observed by mere accident, 
people could not help forming hypotheses to explain 
the resemblance to living beings, and very different 
these hypotheses were. The favourite one was that 
the Great Deluge carried shells, drowned animals, and 
other things about, and in retreating left them scattered 
over the surface of the earth, even upon the tops of 
high mountains. The celebrated Voltaire, on the 
contrary, suggested that the shells found high up in 
the Alps must have been dropped by the pilgrims, 
who used to cross the mountains in former centuries. 
Perhaps a more reasonable hypothesis was to the 
effect that they were "freaks of nature," that is, that 
the resemblance to animals and plants arose from 
accident, just as frost on a window-pane sometimes 
resembles the branches of a tree. A further hypo- 
thesis was that the fossils really consisted of the remains 
of living beings covered up in the mud or sand which 
became the substance of rocks innumerable centuries 
ago. The last hypothesis was selected as the true 
one by the processes of deductive reasoning and 
verification, which I have describedc 

120. We proceed to reason about the hypotheses 
somewhat in this way. If the Great Deluge deposited 
the fossils on mountains, then the fossils ought to be 
found only on the surface or near it, whereas great 
numbers^ of fossils are found in deep mines, driven 
through hard rocks, where the waters of the Deluge 



XV.] INDUCTIVE REASONING. 8i 

cannot have placed them. This hypothesis, therefore, 
is wrong. Nor is that of Voltaire any better ; for 
fossils are found on mountains, and in parts of the 
earth, the Arctic Regions for instance, where pilgrims 
never went, not to speak of the fossils sunk deep in 
the earth. The hypothesis about "freaks of nature" 
is less easy to disprove, and there is no doubt that at 
various times, things have been believed to be fossil 
remains of animals and plants which were not so. 
But we may argue in this way : if, in such a great 
multitude of cases, stones have been formed by mere 
accident in the shapes of living things, there is equal 
reason why they should take by accident the forms of 
other objects. Why should we not meet with fossil 
books, and fossil teapots, and fossil chairs and tables ? 
The hypothesis of freaks of nature does not give 
any reason to expect what we do find, more than 
multitudes of things which we do not find. 

121. The last hypothesis, on the contrary, namely, 
that an immense number of animals and plants have 
lived in past ages, and left their remains buried in the 
strata of sand and mud then deposited in the seas, 
lakes, or rivers, enables us to explain many peculiar 
facts. We see how it is possible that these remains 
should be found at great depths in the crust of the 
earth, one layer of rock after another having been 
formed during many millions of years. We can argue 
in this way too : if an animal be buried in the earth 
at the present day, we know that the flesh and soft 
parts will quickly disappear, and after the lapse of a 
hundred years only the bones, teeth, and hard parts 
will remain. Accordingly, if animals with skeletons 
lived in former geological ages, we ought usually to 
find only the bones and durable parts. And it is a 
fact that we possess the fossil skeletons of multitudes 
of animals whose forms are otherwise unknown to us. 
We meet too with the shells of shell-fish, the hard 



82 PRIMER OF LOGIC. [xv. 

scales of fishes or reptiles, the bark of trees, in short 
just those parts which are most durable. Sometimes 
even the bones (;f an animal have been wholly rotted 
away, and yet the teeth, which are the hardest and 
most indestructible parts of the whole body, remain. 

12 2. We can argue, again, that if shell-fish were 
embedded in mud and then pressed with an immense 
weight of rock gradually formed over them, they ought 
to be compressed and flattened. Accordmgly we do 
find fossil shells sometimes quite flat and broken as if 
by pressure, and the remains of the trunks of trees 
discovered in coal mines are never quite round, but 
partially flattened. In these and many other ways, 
then, we can argue that if animals and plants 
did live millions of years ago, their remains 
would now present appearances which agree 
with what is observed. Hence we are obliged 
to reject all the previous hypotheses, which disagreed 
with facts, and adopt the last hypothesis which so well 
agrees. 

123. Probably the most important law of nature 
ever discovered is that called the Law of Gravity, 
which states that all bodies in space tend to fall 
towards each other with a certain force depending on 
the magnitudes of the bodies and the distance between 
them. It might seem that we need no aid of logic to 
show us that things fall towards the earth, because, 
whether we throw up a stone or a book, a gold coin 
or a feather, they will all descend more or less quickly 
to the surface of the earth. The ancient Greeks 
observed this much, and no doubt the ancient Egyp- 
tians and other peoples before them. But then it 
does not seem to be true that all bodies fall ; for 
flames ascend upwards, and in smoke, and clouds, and 
bubbles we have other exceptions. Aristotle, the 
greatest of Greek philosophers, came to the conclusion 
that some things were naturally heavy and tended to 



XV.] INDUCTIVE REASONING. 83 

fall, while other things were naturally light, and tended 
to rise. Only about two hundred years ago did 
Newton succeed in showing how much better it was 
to make the hypothesis that all things tend to fall, 
because he could then explain not only the motions 
of flame and other apparently light things, but also 
the movements of the moon, sun, and planets. Tf 
we put a pound weight into one scale of a balance, 
and only half-a-pound into the other scale, the latter 
will of course go up as the former is pulled down by 
the greater force. So, if flame be a lighter substance 
than the air around, it will be forced or buoyed up 
like a cork in water. Thus, when we argue deduc- 
tively, we find that what is apparently tending to rise 
upwards may really be tending to fall downwards, but 
is overpowered by the greater tendency of other 
bodies. 

124. Newton argued again in this way: if all 
bodies tend to fall towards each other, all bodies 
ought to fall towards the earth. Now the moon is a 
body, and therefore it ought, according to evident 
reasoning in the manner of the syllogism, to fall 
towards the earth. Why does it not do so, but go on 
revolving round the earth once in every lunar month ? 
It occurred to him that, if the moon were not in some 
way held by the earth, it ought to go off flying away 
in a straight Hne like a stone from a rapidly revolving 
shng. A moving body will move in a straight line 
unless some force obHges it to alter its course. Thus 
it appeared Hkely that in reality ti e moon was always 
falling towards the earth, and that it was this constant 
falling which prevented it from moving off in a straight 
line. Newton then proceeded to prove by most 
ingenious mathematical reasoning that the force of 
gravity, if it were such as he supposed it to be, would 
keep the moon constantly moving round the earth. 
He also showed that, if his hypothesis of gravity were 



84 PRIMER OF LOGIC, [xv 

true, the planets would move round the sun as they 
do. He went on to explaui a great many peculiarities 
in the motions of the planets and their satellites. He 
showed that even the comets though they come and go 
in so apparently irregular a manner, really move in long 
orbits as gravity would make them move. The tides, 
foo, are another peculiar effect of the same force. Thus 
his law became a verified hypothesis, one so entirely 
agreeing with facts that we cannot but beUeve it to 
be correct. It becomes an established law of 
nature, and is sometimes called a theory, but this 
last word, theory, is used with several different mean- 
ings, and we should take care not to be misled by it. 
Here it means only a well-verified hypothesis. 

125. Sometimes it will happen that two or even 
three quite different hypotheses all seem to agree 
with certain facts, so that we are puzzled which to 
select. A little before Newton formed his hypothesis 
of gravity, the celebrated Descartes had also formed 
an hypothesis to explain the motions of the heavenly 
bodies. He suggested that they were carried round 
in kinds of large whirlpools called vortices, and he 
pointed out that all the planets go round the sun 
in the same direction, as they would do in a whirl- 
pool. The satelhtes of Jupiter, then lately discovered 
by Galileo, also seemed to go round Jupiter in a small 
whirlpool, so that the hypothesis was held by many 
philosopners of the time to be a very good one. 
Newton's hypothesis of gravity, however, explained 
the same facts, and it was difficult to decide which 
was the best hypothesis. That of Descartes was much 
more simple and easy to understand ; that of Newton 
explained a great many more facts and in a more 
exact manner. 

When there are thus two hypotheses, one as good 
as the other, we need to discover some fact or thing 
which will agree with one hypothesis and not with 



xvi.j INDUCTIVE REASONING. ^5 

the other, because this immediately enables us to 
decide that the former hypothesis is true and the 
latter false. Newton pointed out that comets do not 
agree in their movements with Descartes' whirlpools, 
because they pass right through the sun's great whirl- 
pool without moving like the planets which rest in it. 
Even when a comet passed through the supposed 
smaller whirlpool of Jupiter, it moved on as if 
there were no such whirlpool. We now know, too, 
that great numbers of comets pass round the sun 
in all directions. Each would require its own sepa- 
rate whirlpool according to Descartes' hypothesis, 
but as there can be only one great whirlpool round 
the sun, namely, that which carries the planets, it 
becomes quite impossible to explain the motions of 
the comets by Descartes' vortices. All the comets 
on the other hand, as far as they have been observed, 
agree with Newton's hypothesis of gravity. 

126. When any fact, like the motion of comets in 
the above case, enables us_ to select one hypothesis 
and reject other ones, the fact is called a Crucial 
Instance, because it serves hke a Crux or Fingerpost, 
to point out the road which we should take. When 
we try an experiment which will decide in favour of 
one hypothesis and against another, it is called an 
Experimentum Crucis. 

XVL— INDUCTIVE REASONING IN ORDINARY 
LIFE. 

127. It is not only in scientific matters that we use 
hypotheses in order to learn, by correspondence with 
factSj what has been happening. We are continually 
arguing in this way in the commonest affairs, and the 
mind often goes through all the four steps of preHmi- 
nary observation, hypothesis, deduction, and verifica- 
tion in a few seconds. For instance, in looking out 



86 PRIMER OF LOGIC, [xvi. 

of the window into the street of a town, I see that 
the pavement is wet, instead of being dry as it was 
an hour before. In all probability I at once consider 
what can have happened to cause the change. 1 
form several hypotheses : rain may have fallen , a 
water-cart may have passed down the street; the 
turncock may have opened the water-pipes in the 
neighbourhood. With great rapidity I draw deduc- 
tions from these hypotheses. A water-cart does 
not usually water the footpaths, but rain would wet 
the footpath on one side at least. Glancing at 
the footpaths I see perhaps that they are dry. Rain 
then is probably not the cause ; to be more sure, 
I glance at the sky, and if I find it apparently clear 
of clouds, this agrees well with the hypothesis of a 
water-cart, and I should be finally convinced if I 
discovered that the wet portions of the street ran in 
broad parallel lines nearly coinciding with the road- 
way, or only slightly overlapping the footway, in 
the manner in which water-carts usually do their 
work. 

128. Inquiries in courts of justice are conducted on 
exactly the same principles. A burglary has been 
committed, and the police come to examine the pre 
mises. This is preliminary observation. They find 
that the entrance has been skilfully effected, and at 
once form hypotheses as to the men supposed to be 
burglars who are at large. They further inquire as to 
the appearance of men seen going about in the neigh- 
bourhood on the night in question. If any suspected 
character agrees in appearance with a man seen, he is 
probably apprehended, because the hypothesis of his 
guilt has received some slight confirmation. His house 
being searched is found to contain a jemmy and a 
few other tools which are used in housebreaking. 
Surely, then, he is a housebreaker; but, if he is 
the one wanted, the ^^ jemmy" in question will pro- 



XVI.] INDUCTIVE REASONING, 87 

bably have been used in breaking open the doors, 
and will have left a mark which should exactly agree 
in size and character with the tool producing it. Here 
is deductive reasoning. I'he tool is carried to the 
house and compared with any marks which can be 
found, and if it agrees there is strong verification. 

129. The Tichborne trial was probably the longest 
and most careful inquiry ever held to decide between 
two hypotheses. One hypothesis was that a certain fat 
man, now in Dartmoor Prison, is Sir Roger Tichborne ; 
another that he is identical with a butcher called 
Arthur Orton. Many persons are said still to beheve 
that he is Sir Roger, but in that case they can have no 
idea what logic or evidence is. Some people believe 
that because Roger's mother and some of his brother 
officers and friends recognised the Claimant as Sir 
Roger, therefore he is so. But many persons also 
SNVore that he was not, and some persons swore that 
he was Arthur Orton. This kind of evidence is 
very uncertain ; for the man was in any case very much 
changed by age. Where people disagreed so much in 
opinion, there was but one way of proceeding safely, 
i.amely to deduce a great many little circumstances 
which ought to be true of the Claimant, things he 
should remember, things he ought to have done, marks 
which should appear on his body, if he were really 
Tichborne. We must compare these with the evidence 
brought forward, and as far as possible w^e must make 
a like comparison with the other hypothesis that the 
Claimant is Arthur Orton. The more slight and 
apparently unimportant these circumstances are, the 
ijetter proofs they make, because it is less likely 
^hat an impostor would think of them. Thus, when 
the Claimant wrote to Lady Tichborne from x\ustralia, 
he addressed her as Mama, whereas Roger had always 
addressed her in letters as Mother, and it is against all 
custom and probability for a man as he grows older to 



88 PRIMER OF LOGIC. [xvi 

substitute Mama for Mother. He was unacquainted at 
first with many things which a man could rarely forget, 
such as the exact name of his own mother, the number 
of his regiment, the name of the vessel in which he 
left England. He was entirely ignorant of French, 
though Roger was brought up in France ; yet he knew 
some Spanish, picked up during a short residence in 
South America. Roger had been taught Latin at 
Stonyhurst, but the Claimant did not know the differ- 
ence between Latin and Greek. 

130. On the other hand there were many slight 
circumstances which agreed with the hypothesis that 
the Claimant was Orton. He said he had suffered 
from St. Vitus' dance, which was true of Orton but 
not of Tichborne. In his will and journal he men- 
tions people known to the Ortons but wholly unknown 
to the Tichborne family, and moreover displays entire 
ignorance of his own Tichborne property. The name 
of the ship in which he says he left England was the 
Jessie Miller, a ship in which it was proved that 
Orton had sailed. And when the Claimant reached 
England he went straight to Wapping and inquired 
after the old butcher who formerly lived there. It is 
impossible, however, to give in a few words any idea 
of the force of the evidence taken in the Tichborne 
trial, because this force arose from the immense number 
of slight facts and coincidences, each of Httle import- 
ance in itself, but all collectively making the proof as 
good as certain. A fibre of hemp will bear only a 
small weight ; but if we twist many fibres into each 
strand, and unite many strands into a rope, we can 
make a cable as strong as we like. So, we can verify 
an hypothesis as completely as any one can desire if 
we can show that it agrees with a great number of 
diverse facts. 



XVII.] OBSERVATION AND EXPERIMENT, 89 



XVII.— OBSERVATION AND EXPERIMENT. 

131. There are commonly said to be two ways in 
which we gain knowledge of the things around us. 
The first way is merely to observe what 
happens without our interference. We notice 
the rise and fall of the tides, and if we remember, or 
set down on paper, the times at which the tide is 
highest on several days in succession, we shall learn 
that high tide is about three quarters of an hour later 
on each day than on the previous day. If we mark 
the heights of the tides, too, we shall ascertain that 
they are greatest at the times of new and full moon. 
In this and a great many other cases, we cannot in 
anyway govern or regulate the things which we notice. 
The motions of the stars and planets, the changes of 
the weather, storms^ earthquakes, volcanoes, meteors, 
are things which go on quite beyond our control. In 
inquiring about such things, then, we can only employ 
simple observation. 

132. When we can manage it, we should make 
experiments, that is,.. we should put together the 
things of which we wish to learn the nature, in such a 
way as to show what the action will be under certain 
known circumstances. In experimenting we 
interfere with things, and then observe the 
result; experimentation is observation with 
something more, namely regulation of the 
things whose behaviour is to be observed. 
The advantages of experiment over mere observation 
are of two kinds. 

133. In the first place, we shall generally know 
much more certainly and accurately with what we are 
dealing, when we make experiments than when we 
simply observe natural events. A chemist may very 



90 PRIMER OF LOGIC. [xvil. 

properly wish to learn the action of carbonic oxide 
gas upon animals and men, when taken into the lungs. 
If he trusted to mere observation, he would have to 
wait until some animal went by accident into a room, 
well, or other place full of the gas. This would only 
rarely happen, and when it did happen, we could 
hardly be sure whether the gas was really carbonic 
oxide gas ; for it would probably be mixed with much 
carbonic acid gas, which is said to be quite different in 
its action on hving beings. By experiment we should 
learn all that we want very quickly, because we might 
fill a glass vessel lull of the pure carbonic oxide gas, 
and put a small animal such as a rat into it, and 
observe the effects exactly. When so many rats and 
other animals are killed every day for less necessary 
purposes, there can be no harm in a chemist killing 
one or two rats, when he may thereby learn something 
exceedingly useful to men and animals for ever after. 
Carbonic oxirfe gas might be very valuable for 
warming and lighting houses at small cost, and thus 
saving the lives of many persons, if it were not apt to 
do harm by escaping and poisoning people. We do 
not know how great the risk is, but proper experiments 
would soon show this. 

134. Nature sometimes seems to make experiments 
for us. Near Naples there is a very curious cave, 
called the Grotto del Cane. Men can walk safely 
into it, but dogs when they enter soon fall down and 
die, unless quickly removed. At first sight, it might 
appear as if there were some substance in the cave 
poisonous to dogs, but not to men. A few facts, 
however, soon negative this hypothesis ; for if a 
man stoop or lie down, so as to bring his mouth 
within a foot of the floor of the cave, he soon shows 
signs of suffocation. All that is observed to happen 
in the cave is easily explained by the fact (Chemistry 
Primer, Art. '^'^ that carbonic acid is considerably 



xvj I. ] OBSER VA TION AND EXPERIMENT, 91 

heavier than air. A chemist can fill a glass jar with 
this gas, and then pour it into another jar, almost as he 
would pour water. A small animal put into such a jar 
will show signs of suffocation when the carbonic acid 
is poured in, and this experiment completely explains 
what is observed in the Grotto del Cane. 

135. It is a further advantage of artificial experi- 
ments, that they enable us to discover entirely 
new substances and to learn their properties. 
On the surface of the earth, there is always some 
chemical action going on among the earth, and sand, 
and water, but it is the same as has been going 
on for many thousands of years. It is when we 
choose particular substances and heat them, or press 
them, or electrify them in an unusual manner, that we 
may expect to meet something new. It must have 
been a surprising discovery when iron was first made 
from heavy red stones put into a hot charcoal fire ; from 
this and a series of other experiments, we have gained 
all that iron tools, iron vessels, engines, railways, and 
steam-boats now do for us. Gold was probably 
discovered by mere accidental observation, because it 
is in many places found among the sands of rivers. 
But mere observation could never have led us to 
expect that from dull clay we could get a beautiful, 
strong, and very light metal, named aluminium. It 
is quite possible that careful and persevering experi- 
ments will some day lead to the discovery of an 
alloy of aluminium, or of some metal now rare 
or unknown, which will be more useful than all our 
gold and silver. We must not suppose that we have 
yet found out the thousandth part of the wonderful 
things which may be in time discovered by truly 
scientific reasoning and experiment. 



92 PRIMER OF LOGIC. [xviii. 



XVIII.— ANTECEDENTS AND CAUSES OF 
EVENTS. 

136. What we want to do, both in observing and 
experimenting, is to discover the exact circum- 
stances in which an event will happen. In 

other words, we want to know what things must be 
present in order that something else shall appear. 
All the objects which are put together in making an 
experiment, or all the circumstances which precede 
some natural event, such as a thunder-storm, may be 
called antecedents, or the things going before. 
All that happens or is produced afterwards are called 
consequents. In the case of the thunder-storm, 
warm moist air, a bright sun, lofty swelling clouds, 
and a fall of the barometer, are usually the antecedents, 
and a heavy shower of rain, lightning, thunder, a 
squall of cool wind, and a rise of the barometer, are 
consequents. But it is not to be supposed that all 
the antecedents of an event will be necessary for its 
production. The sun might often be shining brightly 
before a thunder-storm, but sometimes such storms 
happen in the middle of the night. The sun, therefore, 
seems not to be needed to produce the storm. If a 
person be taken ill after eating dinner, all the meats 
and drinks — beef, potatoes, cabbages, bread, mustard, 
pepper, salt, water, beer, wine, or whatever else he 
may have taken — will be antecedents, and his illness is 
one of the consequents. But it is exceedingly unlikely 
that there would have been something poisonous in 
each of the dishes and drinks. What we shall need 
to do in such a case is to find out in what particular 
substance the poison was contained, which was the 
necessary antecedent, or, as it is usually called, the 
cause of his illness. 

137. The cause of an event is that antece- 
dent, or set of antecedents, from w^hich the 



xviii.i ANTECEDENTS AND CAUSES. 93 

event always follows. People often make much 
difficulty about understanding what the cause of an 
event means, but it really means nothing beyond the 
things which must exist before in order that 
the event shall happen afterwards. Sometimes 
it may seem as if one single antecedent is the sufficient 
cause. If there be copper in the pickles eaten at a 
meal, it may seem to be the sole cause of the illness of 
the eater. But the peculiar formation of the stomach, 
which becomes deranged by the presence of copper, 
is also a necessary antecedent Copper ^ does not 
poison us when we merely go near it. A single spark 
may seem to be the cause of the explosion of a barrel 
of gunpowder ; but then the gunpowder is equally the 
cause of explosion, and several substances are requisite 
to make gunpowder. We shall in vain attempt to 
produce an explosion v. ith charcoal, or saltpetre, or 
sulphur taken separately. But if we grind them all 
up together in particular proportions, and make the 
mixture into grains, weget something which will explode, 
that is, very rapidly burn, when a spark falls upon it. 
Thus the sulphur, the saltpetre, the charcoal, the 
particular form of the grains, the spark, and, it may be 
added, the absence of moisture, are all necessary 
antecedents or causes of the explosion. 

138. The great rule in making experiments 
is to vary one thing at a time. Our purpose is 
to ascertain exactly which antecedests of an event 
are requisite to produce it. But if I alter two or more 
antecedents at the same time, and the result is altered, 
I cannot tell whether the change is due to one ante- 
cedent, or to the other, or, it may be, to both. If a cup 
of tea does not taste well, it may be due either to the 
poor quality of the tea, or to the water not boihng when 
it was made. If I have a new pot of tea made with 
boiling water and a different kind of tea, I may get a 
better cup of tea, but I shall not learn why the former 



94 PRIMER OF LOGIC. [xviii. 

cup was bad. I must first try the original kind of tea 
with boiling water, and if it still tastes bad, I shall know 
that the fault was in the tea. 

If a person in perfect health falls down stairs, and 
receives severe injuries, followed by death, we feel 
sure that the fall caused the death. But if a person 
is seized with some kind of fit and then falls down, 
and dies soon after, the fatal result may be due either 
to the fall or the fit, or to both, and the minutest 
inquiry may hardly settle which is the case. 

139. Every one knows that a bright piece of iron 
soon rusts when exposed to the air. What are the 
causes of this rusting ? If we put a piece of bright 
iron into a glass tube, exhaust the air out of it, and 
seal the tube up, the brightness of the metal will 
remain undimmed for any length of time. But air is a 
mixture of oxygen, nitrogen, vapour of water, carbonic 
acid, and small quantities of other substances. The 
air always contains, too, a very slight quantity ol 
common salt, in small particles which float about. 
Any of these substances, then, may be causes of the 
rusting of iron, and to decide which are the causes, it 
is not sufficient to withdraw air altogether, nor even to 
try pieces of iron with pure oxygen, nitrogen, and 
vapour of water separately. It will be found that the 
iron does not rust with any of these substances when 
quite pure. The most instructive experiment is to 
take common ajr and remove all the moisture from it ; 
iron will remain perfectly bright in such air, so that 
moisture is one of the causes of rusting. But 
it is not the only cause ; for in perfectly pure water, or 
vapour of water, free from oxygen and carbonic acid, 
iron also remains bright. In a mixture of oxygen, 
watery vapour, and carbonic acid, such as air would 
be without the nitrogen, iron rapidly rusts. By further 
similar experiments we should be led to conclude that 
two substances, oxygen and vapour of water, are 



XIX.] DISCOVERY OF AGREEMENT, 95 

necessary antecedents of the rusting of iron, and that 
carbonic acid, if not altogether necessary, makes iron 
rust much more rapidly. This instance shows that it 
is not always easy to find out exactly which of the 
many antecedents of an effect are the necessary ante- 
cedents or causes of the effect 

XIX.— DISCOVERY OF AGREEMENT. 

140. What we want to do both in observing and 
experimenting, as we have learnt in the last Article, is 
to discover the circumstances which always precede 
an event. The first step towards this discovery is 
usually to try and find out what there is alike in the 
antecedents of every particular case when the event 
occurred. Accordingly, when we wish to explain the 
occurrence of anything, ^ve should begin by 
thinking of everything hke it that we have 
ever seen or heard of, and then we should compare 
these things together carefully, and try to detect the 
exact likenesses between them. 

141. Suppose that we see a bright rainbow in the 
sky, and want to learn exactly why it occurs then and 
not at other times. We want to know, in short, what 
are the causes of its occurrence. We must begin by 
comparing together all the occasions we can remember 
when a rainbow was seen. We may observe that 
whenever such a bow appeared, rain was falling some- 
where in the sky. As the name implies, the rainbow 
always occurs on or among rain drops, and no one 
ever saw a rainbow with a perfectly clear sky. At the 
same time, clouds and rain must not obscure the whole 
sky. The sun must be shining while the rain is falling. 
We may easily remember that rainbows occur with 
occasional brief showers of rain, or when a storm is 
nearly at an end, and the sun is beginning to shine 
forth again. 



96 PRIMER OF LOGIC. [xix. 

142. We ought not to content ourselves with 
considering ordinary rainbows only ; we should think 
and collect information about all cases in which similar 
coloured bows, or even similar colours, are produced. 
Lunar rainbows are sometimes seen, and when seen 
there is a bright full moon shining on a shower of rain. 
Comparing lunar with solar rainbows, we find that 
the sun is not requisite, but that any bright beam of 
light shining upon a shower of ram seems to be the 
necessary antecedent. Nor is rain falling from the 
sky quite necessary. Some waterfalls — especially the 
Rjukan or Smoking Foss in Norway — throw up 
clouds ot fine spray composed of minute particles of 
water. If we see the sun shining in a particular 
direction upon such spray a bright bow, exactly like a 
rainbow, is discovered. The fine drops of water from 
a fountain occasionally show fragments of a similar bow. 
In the early morning the grasSp and shrubs, and spiders' 
webs are sometimes covered with drops of dew, and a 
bright sunbeam produces upon them a rainbow turned 
upside down, At sea the colours of the rainbow may 
be seen upon the spray as it is driven above the surface 
of the sea by the wind after a storm. 

Comparing the different occasions on which the 
same sort of bow is seen, we discover that a beam 
of light and particles of water, in a particular 
position are the necessary antecedents or 
causes of the bow of colours. This is nearly all 
that simple observation can tell us, and it forms merely 
the first step of preliminary observation. 

143. It was Sir Isaac Newton who fully explained 
how rainbows are produced, and this he did by means 
of hypotheses. Long before his time, indeed, it was 
remarked that colours, similar in their succession to 
the seven colours of the rainbow, are seen in sharply 
cut glass vessels, diamonds, or other transparent 
objects. Roger Bacon whom I mentioned before 



XX.] VARIATIONS. 97 

(Art. no), had discovered the circumstances in which 
a rainbow appears, and had also remarked the 
resemblance to the colours of crystals. Another 
early experimenter pointed out that similar effects 
are produced by a sunbeam falling on a glass globe 
full of water. But Newton did a great deal more ; 
for he imagined the different ways in which a ray 
of light might enter a drop of water and get out 
again, so as to reach the observer's eye, after having 
been reflected and refracted within the drop. Knowing 
the laws of the reflection and refraction of light, he 
was able to calculate the angle between the ray coming 
out and that going in, and thus to decide the size and 
position of a rainbow, with respect to the sun and the 
eye of the observer. 

144. Measurements of rainbows agreed with 
Newton's calculations ; but he was not contented with 
this verification alone. He proved that a second, but 
smaller portion of the light entering a drop of rain, 
would come out in a different direction, so as, when 
bright enough, to form another larger rainbow. It is 
well known that a rainbow when very brilliant is often 
accompanied by a second fainter bow, and in this we 
have a complete verification of Newton's theory. In 
such a case we can see clearly how philosophers, 
beginning with simple preliminary observation, 
gradually went through all the steps mentioned in 
Article 118, and, by hypothesis, deduction, and verifi- 
cation, arrived at a true theory. 

XX.— THINGS WHICH VARY IN QUANTITY. 

145. The causes and effects with which we have to 
deal in science can often be made to vary in quantity. 
We can make a body more or less hot or cold ; we can 
put a greater or less weight to press upon it ; or we can 
try how much a magnet of greater or less force will 

7 



98 PRIMER OF LOGIC. 



[xx. 



attract it. Whenever we can thus alter the quantity ot 
the things experimented on, we can apply a rule for 
discovering which are causes and which are effects. 
We must vary the quantity of one thing, 
making it at one time greater and at another 
time less, and if we observe any other thing 
which varies just at the same times, it will 
in all probability be an effect. 

We may easily observe, for instance, that when air 
IS forced into a fire by use of the bellows, greater heat 
IS produced ; the more powerfully we blow, the hotter 
the fire becomes, and as soon as we leave off blowing, 
the fire begins to cool. There can be no doubt, then,' 
that a supply of air is one of the causes of the com- 
bustion of fuel. In the same way we may easily prove 
that sunhght is one necessary condition of the growth 
of plants. The sun partly makes the experiment for 
us in this case, because it shines so much more 
powerfully, and for a longer time, in summer, than in 
wmter, and we see that grass and plants grow rapidly 
m June and July, and hardly at all in December and 
January. But this is not quite satisfactory, because 
the air is much warmer in summer than in winter, and 
this might perhaps be the reason. 

To sadsfy ourselves, we ought to make more exact 
experiments, by taking several plants of exactly the 
same kind, planted in similar pots containing similar 
soil, putting some plants where they will receive bright 
sunshine, others where they will be partially shaded, 
as under trees, and some again under boxes or in 
sheds, where they will have little or no light, but where 
the air will be of the same temperature as outside. 
Then, as nearly as can be expected, the growth of the 
plants will be found to correspond to the quantity ot 
sunshine falling upon them. 

146. From the foregoing example we may learn the 
need of the precaution, to vary only one thing at 



XXI.] VARIATIONS. 99 

a time, as far as we can possibly manage it. This is, 
in fact, the same precaution which we had to take in 
simple experiments (Art. 138), putting one thing 
in operation at once. Now we must make one cause 
greater and less, keeping all the other things which 
are present of the same quantity as exactly as we can. 
If we were to put one plant where it would have both 
more sunshine and more moisture than another 
similar plant, we could not be sure whether the 
difference of growth was due to the difference of sun- 
shine, or to the difference of moisture. If possible 
then we should try plants having equal quantities of 
moisture, and in every other respect alike, with 
different quantities of sunshine. Then again, if we 
want to know the effect of moisture, we should take 
similar plants, similarly supplied with sunshine^ and 
differing only in the supply of moisture. 

XXL— THINGS WHICH VARY PERIODICALLY. 

147. The changes and motions which things about 
us exhibit are often what we call periodic, that is, 
they happen over and over again in a similar manner 
after equal periods or intervals of time. Day and 
night are periodic changes, for they happen alternately, 
and one night is nearly equal in length to the pre- 
ceding or following night. But, as summer approaches, 
the daylight grows longer, and the nights shorter ; 
this happens in almost exactly the same way every year, 
so that it is also a periodic change, depending upon 
the motion of the earth round the sun. The tides also 
rising twice a day are periodic. 

148. When things thus vary regularly and frequently, 
there is a simple rule, by following which we can 
judge whether changes are connected together as 
causes and events. Those things which change 
in exactly equal times are in all likelihood 

LofC. 



loo PRIMER OF LOGIC, [xxi. 

connected together. Almost every day the air 
becomes warmer in some degree during the afternoon, 
and when we take the average of several weeks or 
months, we find that it is almost always warmest about 
three o'clock in the afternoon. There can be no 
reasonable doubt, of course, that this increase of heat 
is caused by the sun, which is at its highest point in 
the heavens about twelve o'clock, but continues to 
warm the air more than it is cooled, for three hours 
afterwards. In the same way the warmest day in the 
year is about the 21st July, and this is, on the average, 
at an equal interval from the 21st June, the longest day. 
Even if we did not on other grounds know it to be the 
case, we should infer that the warmth of summer is due 
to that periodic motion of the earth round the sun, which 
causes the sun to shine longer and brighter during 
summer than during winter. 

149. In other cases we learn from periodic changes 
that most unexpected things are connected together. I 
have mentioned the tides as periodic events ; now, as 
the tides happen at intervals of about I2f hours, 
whereas the sun goes round the heavens at intervals of 
about 24 hours, we cannot conclude by our rule that 
the sun is the cause of the tides in question. We 
have to look out for some other cause which varies, or 
moves round in I2f hours. We should not meet with 
anything exactly answering this description ; but we 
should find that the moon gets nearly to the same 
place in the heavens on successive evenings at intervals 
double that named, or 24f hours. 

When the moon is quite new, it is seen early in the 
afternoon ; but as it grows older and older, it rises 
later, until at last it is not seen at all till early morning. 
If, when conveniently seen in the evening, we noted 
the time of its reaching a certain position in the heavens 
we should find the time to be three quarters of an 
hour later every night. The tides are just so much 



XXL] VARIATIOXS. loi 

later also ; hence it becomes very probable that the 
attraction of the moon on the ocean is the cause of 
the tides. Sir Isaac Newton showed beyond all doubt 
that this was the case, and he explained why there are 
two tides in the 24I hours instead of one tide. 

150. In the last thirty or forty years very curious 
discoveries have been made about variations in the 
atmospheres of the sun and earth. It was well known 
to Sir William Herschel and other astronomers, seventy 
years ago, that the spots on the sun's face are much 
more numerous and large in some years than in others. 
Careful observers having registered the spots for many 
years, discovered by degrees that the years in which 
the spots are very numerous, happen at intervals of 
about eleven years. There were a great many spots 
in 1837, in 1848, in 1859, and in 1870, and com- 
paratively few in the intermediate years, about 1842, 
1853, and 1864. It was also noticed that those 
wonderful and unaccountable displays of light in the 
heavens, called Auroras, are much more frequent and 
grand in some years than" in other years. Strange to 
say, when there are many sun-spots there are many 
fine .\uroras, as in the autumn of 1859, and again in 
1870, It is impossible to say at the present time how 
spots in the sun can cause Auroras ; but they vary 
together so regularly that there can hardly be any 
doubt about their being connected together. 

There is now reason to believe that the typhoons, or 
great st3rms which occur in parts of the tropical re- 
gions of the earth, also depend upon the sun-spots. 
Meteorologists are endeavouring to discover whether 
the comparative coldness or warmth of some years, or 
the variations in the quantity of rain, may not also 
have some connection with the spots on the sun, but 
we ought to be very careful in drawing conclusions 
about such uncertain changes. Sir William Herschel 
thought that the variations in the price of corn 



ro2 PRIMER OF LOGIC. [xxu. 

depended upon those of the sun-spots, and this, if 
proved, would be a very interesting and important 
discovery. I have tried to ascertain whether it is so 
or not, but have been unable to find any evidence of 
the truth of Sir W. Herschel's hypothesis. 



XXII.— REASONING FROM EXPERIMENTS. 

151. It would be a mistake to suppose that the 
making of an experiment is inductive reasoning, and 
gives us without further trouble the laws of nature. 
Experiments onl/ give us the facts upon 
which we may afterwards reason. If I wrap 
up a piece of ice in a blanket and, placing it alongside 
of another piece of ice not wrapped up, observe that 
the latter rapidly melts away, and the former does not, 
there are only two observations here. If I were to 
draw the conclusion that a piece of ice wrapped up in 
a blanket always melts less rapidly than one not 
wrapped up, this would be a case of inductive reason- 
ing, but a bad case, because it would not always hold 
true. If the temperature of the surrounding air. and of 
other objects, were below the freezing point, neither 
of the pieces of ice would melt. 

152. Experiments then merely give facts, and it is 
only by careful reasoning that we can learn when the 
same facts will be observed again. The general 
rule is that the same causes will produce the 
same eflfects. Whatever happens in one case will 
happen m all like cases, provided that they are really 
like, and not merely apparently so. The advantage 
of being able to try experiments is that we ascertain 
exactly what are the antecedents and surrounding 
circumstances of an experiment, and we can vary these 
so as to find out which are important and which are 
not. If we wished to decide exactly in what circum- 



XXII.] EXPERIMENTS, 103 

stances the melting of ice would again be observed, 
we should have to mark the temperature of the air, and 
try the experiment over and over again at different 
temperatures. We should also have to consider whether 
the sun was shining, or whether heat could reach the 
ice from fires, or warm bodies in the neighbour- 
hood. 

153. When we have by repeated experiments tried 
the effect which all the surrounding things might have 
on the result, we can then reason with much confidence 
as to similar results in similar circumstances. But we 
can never be quite sure about the matter. It is 
always possible that we have overlooked the thing 
which is really necessary to the result of the experiment. 
It may be very unlikely, but it is possible. Now and 
then chemists find that some experiment which they 
thought they understood completely, deceives them and 
gives quite unexpected results. Sometimes they can 
afterwards explain these exceptions and failures. They 
may happen to have met with a new substance which 
looked like another substance familiar to them, but 
was really different in its properties. This is the usual 
way in which new elements are discovered. 

154. In order that we may, from our observations 
and experiments, learn the laws of nature and become 
able to foresee the future, v/e must perform the process 
of generalization. To generalize is to draw 
a general law from particular cases, and to 
infer that what we see to be true of a few 
things is true of the whole genus or class to 
which these things belong. It requires much 
judgment and skill to generalize correctly, because 
everything depends upon the number and character of 
the instances about which we reasoHc 



i04 PRIMER OF LOGIC. ' [xxiJj. 



XXIII —HOW AND WHEN TO GENERALIZE. 

155. It is very difficult to explain how it is that we 
can ever reason from one thing to a class of things by 
generalization, when we cannot really be sure that the 
things resemble each other in the important points. 
A wine merchant generahzes on a small scale, when 
he takes a single glass out of a pipe of wine, and infers 
that the quality of every other glassful drawn from the 
same pipe will resemble this particular glassful. But 
then he knows that the wine in the pipe has been well 
mixed up,- so as to be exactly alike in all parts. 
Similarly a broker who sells cotton, corn or sugar, has 
a sample taken which fairly correspond , to the whole 
of the lot of goods, and the buyer takes the goods on 
the belief that the sample is really a fair one. 

156. Who is to say what is a fair sample of things 
m nature ? Can we say that, because all the stones 
observed by us fall to the ground again when . 
thrown up, therefore all other stones will do the 
same ? If so, upon what grounds do we argue ? We 
have to get a general law from particular facts. In 
reality this can only be done by going through all the 
steps of inductive reasoning as explained in Articles 
112 to 118. Having made certain observations, we 
must frame hypotheses as to the circumstances, or laws 
from which they proceed. Then we must reason 
deductively, and, after verifying the deductions in as 
many cases as possible, we shall know how far we can 
trust similar deductions concerning future events. 
But this long process has been performed very fre- 
quently by philosophers, and it usually leads to the 
conclusion, that things which resemble each 
other in several of their properties will 
probably resemble each other in more pro- 
perties. There is no certainty in the matter. 



XXIII.] GENERALIZATION, 105 

and as I have already said, it is difficult to judge when 
we may, and when we may not, safely infer from some 
things to others in this simple way, without making a 
complete theory of the matter. 

157. The only rule that can be given to assist us is 
that if things resemble each other in a few 
properties only, we must observe many in- 
stances before inferring that these properties 
will always be joined together in other cases. 
We notice that stones when thrown into the air, fall 
to the ground, and the same is true of pieces of wood, 
metal, ice, leaves of trees, feathers, or scraps of paper ; 
even spiders' webs, and the lightest things do the same 
when not prevented by wind. All these are material 
solid bodies, and we may observe that the circumstance 
of falling to the earth does not seem to be connected 
with the colour, size, shape or other peculiarities of 
the things. The things, in short, which fall, resemble 
each other in no apparent circumstances except that 
they do fall, and that they are solid and material. 
Further observations sho\v'that liquids also fall, as in 
the case of rain. Clouds, smoke, steam, and dust 
seem not to fall ; but further inquiry shows that in all 
these cases the particles are really falling as rapidly as 
the air will allow them. Moreover, the air itself falls 
very rapidly, when there is an empty space or vacuum 
into which it can fall. Thus we find that even solidity 
is not necessary to the property of falling, but that all 
bodies, which consist of matter at all, also have weight. 
These circumstances having been so often joined 
together, we are justified in expecting that they will be 
joined together in all future cases which we may be 
able to observe. We conclude, therefore, that all 
material bodies will have the property of falling in 
the same manner as the stones and other things ob- 
served. In other words, we learn the general law that 
all things which resemble each other in being material, 



/o6 PRIMER OF LOGIC. [xxiii. 

will also resemble each other in the property of 
falling towards the earth, when not prevented by any 
other force. This is a very perfect instance of 
gencraUzation, and the conclusion ha^ been confirmed 
by Newton's hypothesis of gravitation, and the ob- 
servations made on the motions of the heavenly 
bodies. 

158. As a second instance of a good generalization, 
let us consider what we can infer about the bright 
colours seen upon soap bubbles. If we were to 
generaHze carelessly, we should perhaps infer that all 
soapy water ought to show bright colours ; but on 
examining the soapy water which we used, we should 
find ourselves wrong. To know when to expect 
similar colours, we must take every opportunity of 
observing the same thing again. When tar is spread 
in a thin film over water, as may sometimes be seen 
in canals and docks, it also shows most beautiful 
colours of the same kind. Now the film of tar does 
not seem to resemble a soap bubble in anything but 
being very thin. When a piece of thick glass is 
cracked, and we examine the crack very carefully, we 
shall often find colours similar in appearance, though 
perhaps less brilliant ; and, if we press two plates of 
glass together, or still better, press a nearly flat lense 
upon a piece of plate glass, colours are seen near the 
place where the two pieces of glass touch. It is difficult 
to say in what way tar, soapy water, and cracks in glass 
resemble each other, unless it occurs to us that between 
the two surfaces of the glass there is a thin space 
filled with air. The colours thus appear in three cases 
where light falls upon a very ihin film of substance 
with two bright surfaces close together. Further 
inquiry would show that this was a good case for 
generalization, and that any very thin transparent plate 
upon which light falls, will produce similar colours. 
When we see such colours, then, we may expect that 



xxiv.J REASONING BY ANALOGY. 107 

there will be found thin plates of substance. The 
bright colours of mother-of-pearl arise in this way 
from the extreme thinness of the layers of which the 
shell is formed. 



XXIV.-REASONING BY ANALOGY. 

159. At the beginning of this Primer, I described 
the way in which we commonly reason, from one 
thing directly to another (Articles 4 to 6), as from the 
mountains of California to those of New South Wales, 
or from one orange to another. This kind of reasoning 
may be called Reasoning by Analogy, and it only 
differs in degree from that kind of reasoning called 
generalization. When many things resemble 
each other in a few properties, we argue 
about them by generalization. When a few 
things resemble each other in many proper- 
ties, it is a case of analogy. If only a very few 
things resemble each other in a few points, we should 
have no ground for arguing from them to other things. 
But when there are either a number of things showing 
resemblance, or a number of properties in which they 
show resemblance, then we have some grounds for 
inferring that the same properties will be found joined 
together in other cases. The rule for reasoning 
by analogy is, then, that if two or more things 
resemble each other in many points, they 
will probably resemble each other also in 
more points. 

160. If I see a machine with boiler, cylinder, air- 
pump, piston-rod, crank, and other parts exacdy 
resembling those of a steam-engine, I do not hesitate 
to call it a steam-engine, to assert that it has a piston, 
valves, and other hidden parts, like all steam-engines. 
It is in the same way that we reason about the sub- 



io8 PRIMER OF LOGIC, [xxvr. 

Stance of which anything is made. If a person offers 
me a shiUing as change, how can I be sure that it is a 
good shining, and made of silver ? All that I can do 
is to examine the coin, and observe whether it has a 
fine pure white lustre where the surface is rubbed; 
whether there is in other parts of the surface the black 
tarnish peculiar to silver ; whether the coin seems to 
be hard, and gives a sharp ringing sound when thrown 
down. If it has all these characters and, m^oreover, 
has a good impression exactly like that seen on other 
shillings issued from the mint, then it is doubtless 
made of silver, and is a true shilling, that is to say, it 
will show all the other properties of standard silver, 
when examined in a manner suited for showing them. 
1 6 1. In spite of the very distinct marks by which 
we may usually recognise a silver coin, we know that 
counterfeit ones are often made and passed from one 
person to another. In these and many other cases 
reasoning by analogy is found to be a very 
uncertain guide. In some cases unfortunate 
mistakes are committed. Children are sometimes 
killed by gathering and eating poisonous berries, 
wrongly inferring -that they can be eaten, because 
other berries, of a somewhat similar appearance, have 
been found agreeable and harmless. Poisonous toad- 
stools are occasionally mistaken for mushrooms, 
especially by people not accustomed to gather them. 
In Norway mushrooms are seldom seen, and are 
not eaten ; but when I once found a few there, and 
had them cooked at an inn, I was amused by the 
people of the inn, who went and collected toadstools 
and wanted me to eat them also. This was clearly a 
case of mistaken reasoning by analogy. Even brute 
animals reason in the same way in some degree. The 
beaten dog fears every stick, and there are few dogs 
which will not run away when you pretend to pick up 
a stone, even if there be no stone to pick up. 



KKW.] REASONING BY ANALOGY, 109 

162. In science a great deal is learnt by analogy. 
We know that the moon has mountains, because there 
are marks on the face of the moon, which closely 
resemble the appearances which our mountains would 
have as seen from the moon. The moon's moun- 
tains cast longer shadows as the sun is setting, and 
shorter ones as it is rising, just as it happens on the 
earth's surface. But the ancient astronomers were 
misled by analogy into thinking that the flat dark 
spaces on the moon's surface were seas ; they thought 
that the moon would naturally have oceans and seas 
of various sizes, like the earth. By the use of large 
telescopes we now know that there are no seas, rivers, 
or other preceptible bodies of water on the moon. 
(Primer of Astronomy, Art. 129.) 

163. Sometimes the analogy between things is so 
complete and exact that we cannot doubt it for a 
moment. The Chinese have printed mathematical 
tables of numbers called logarithms ; but on examining 
these tables they were found ta have the same mistakes 
as some English tables of logarithms. The analogy 
was so complete that we must believe the Chinese 
tables to be copied from the Enghsh ones. This is 
the only hypothesis which can explain the resemblance. 
As we walk over the flags in a street, we may often 
notice that the surface is wavy, in a manner exactly 
resembling a fine sandy sea beach, from which the 
tide has just receded. Sometimes we mpvy notice on 
flagstones httle pits or hollows, ahke in form and size to 
the holes which large drops of rain make in a sandy 
surface. The tracks of insects also and the foot-prints 
of birds, and other animals are sometimes seen. We 
cannot explain these precise analogies between the 
iiagstones and the sea beach, except by supposing that 
the flagstones really were formed of the sand and mud 
rleposited by waves upon a sea beach countless ages 
ago. Geologists continually argue by analogy in this 



no PRIMER OF LOGIC. [xxiv. 

way from what goes on under their eyes in the present 
day to what must have happened when the hardest 
rocks were being slowly formed. 

164. Of all the planets Mars seems to have the 
closest analogy to the earth. When carefully examined 
it is found to have darker portions, believed to be seas, 
and lighter portions which are probably land. At 
each pole of the planet, too, is a white round patch ; 
now each of these patches, if carefully watched, is 
found to decrease when Mars is in such a position as 
to expose the spot to the sun's rays, and to increase at 
other times. These white spots thus behave exactly 
like the masses of snow and ice at the north and 
south poles of the earth. The analogy is so perfect 
that we conclude, almost beyond doubt, that Mars has 
regions of ice and snow at its poles like the earth. 
(Primer of Astronomy, Art. 162.) 

165. There is no way in which we can 
really assure ourselves that we are arguing 
safely by analogy. The only rule that can be 
given is this, that the more closely two things resemble 
each other, the more likely it is that they are the same 
in other respects, especially in points closely connected 
with those observed. Not only is it very probable 
that the spots on Mars are composed of ice and snow, 
but we may also infer that Mars has an atmosphere 
with winds, clouds, rain, and other things very like 
our own. Some people argue, too, by analogy that 
there are probably living beings on Mars more or less 
resembling the plants and animals on the earth ; but it 
is evident that reasoning on such a matter is very 
uncertain. In order to be clear about our conclusions, 
we ought in fact never to rest satisfied with mere 
analogy, but ought to try to discover the general laws 
governing the case. 

166. In analogy we seem to reason from one fact to 
another fact without troubling ourselves either with 



XXIV.] REASONING BY ANALOGY, iii 

deduction or induction. But it is only by a kind of 
guess that we do so ; it is not really conclusive reason- 
ing. We ought properly to ascertain what general 
laws of nature are shown to exist by the facts observed, 
and then infer what will happen according to these 
laws. This we can do in the case of the white spots 
on Mars to a great extent. We know very well that 
the rays of the sun melt snow and ice, and we observe 
exactly how in the Arctic regions these effects take 
place. We are therefore prepared to explain the 
increase and decrease of the white spots of Mars by 
reasoning deductively. But this does not apply to the 
supposed inhabitants of Mars. No one has ever been 
able to discover how living beings came to exist on 
the earth, and no one can be proved to have produced 
a living creature out of dead matter. We cannot 
therefore argue deductively that living beings would 
be produced on Mars, because its surface and atmo- 
sphere are in some ways like those of the earth. 

167. In other matters people are continually led 
into errors by trusting to slight analogies. A few 
years ago it was common to hear it asserted that the 
government would make profit by sending telegrams 
at very small charges. It has even been said that the 
railway companies ought to carry passengers any dis- 
tance at the same low charges which are required for 
letters and books. These people point to the Post 
Office as an institution which earns for the govern- 
ment a large profit although it only charges a penny 
for a letter, and a halfpenny for a card or newspapero 
They say, too, that as the prices of the daily news- 
ipapers were in past years gradually reduced from six- 
pence to one penny, the proprietors got larger profits. 
Then by analogy they infer that the same will happen 
with telegraphs and railways. But this is a mere guess, 
;a,nd a very bad one. They ought not to be satisfied 
with mere apparent resemblance, but should inquire 



1 1 2 PRIMER OF LO GIC. [xx v. 

into the reasons why the penny post and the penny 
newspapers pay so well. 

i68. They would find, for instance, that it is not the 
pennies paid for newspapers which make the profits of 
the publishers, but the large sums of money which are 
received for advertisements. In telegraphs and rail- 
ways there is little or no source of profit analogous to 
advertisements. They would find, again, that the Post 
Office is very profitable to the government, because a 
postman can carry a great many letters and cards at 
the same time, and can deliver a bundle of half-a- 
dozen almost as quickly as a single one. The Post 
Office, therefore, can usually do more work without 
employing more men, and the more letters it de- 
livers the greater is the profit. With the telegraphs, 
however, it is quite difi'erent. A clerk cannot telegraph 
a dozen messages along the wires at once, nor even 
two messages. Each message has to be sent sepa- 
rately and delivered generally by a messenger employed 
for this single purpose. The more messages are sent 
the more clerks and messengers are needed. If the 
charges were to be made very low, the government 
would lose a great deal, instead of gaining as they 
do in the Post Office. We find then that reasoning 
by analogy is not to be depended upon, unless we 
make such an inquiry into the causes and laws of the 
things in question, that we really employ inductive and 
deductive reasoning. 



XXV.— FALLACIES. 

169. In learning how to do right it is always desir- 
able to be informed as to the ways in which we are 
likely to go wrong. In describing to a man the road 
which he should follow, we ought to tell him not only 
the turnings which he is to take, but also the turnings 



KKV.] FALLACIES, if- 

which lie is to avoid. Similarly it is a useful part of 
logic which teaches us the ways and turnings by which 
people most commonly go astray in reasoning. 

170. Errors and mistakes in reasoning are 
called fallacies, that is, modes of reasoning which 
deceive. But we ought not to confuse a false opinion 
with the bad reasoning by which it is reached. The 
word fallacy is in fact an ambiguous one (Art. 29). 
In one sense it is a fallacy that the moon governs the 
weather, because long and careful inquiries have shown 
that there is no correspondence between the changes 
of the moon and the changes of the weather. But 
this is a fallacious or false opinion : the logical fallacy 
consists in the bad reasoning which has by degrees led 
people to believe in the moon's power. On one or 
two occasions a person may notice a change of weather 
on the day of new moon, and he thinks it so singular 
that he tells his neighbours of the fact, and they re- 
member perhaps to have noticed the same thing once 
or twice. But it is bad reasoning to argue that, be- 
cause on a few occasions things happen one after the 
other, therefore the one is the cause of the other. 

171. There are at least twelve new moons in each 
year, and changes of the weather take place in this 
country at least once a week on the average. It is 
therefore quite likely that a new moon and a change of 
the weather will happen together now and then. But 
most people believe that the moon affects the weather 
not because they have really noticed it to be so, but be- 
cause they have often heard it said to be so. This is 
not bad reasoning, like that which gave rise to the 
false belief, but it is simply repeating the same false 
opinion. In logic we ought to use the word fallacy to 
mean only false reasoning, and not false beliefs. 

172. Taking the word fallacy, then, to mean bad 
reasoning, we must remember that several different 
ways of failing into erroneous reasoning were described 



114 PRIMER OF LOGIC, [xxvi. 

in the Articles on deductive logic. Whenever we 
break the rules for converting 'propositions, the rules 
of the syllogism, or any of the other rules which were 
given for guiding us in making inferences, we commit 
a fallacy. If we infer that, because all the ordinary 
animals known to us have the power of moving them- 
selves, therefore this object which has the power of 
moving itself is an animal, this is against the third rule 
of the syllogism, and is a case of the fallacy of undis- 
tributed middle term (Art. 85). Each of the other 
rules of the syllogism, when broken, gives rise to a 
distinct kind of fallacy : a breach of the first rule is 
called a Fallacy of Four Terms : if we attempt to 
draw a conclusion from two negative premises, there is 
said to be a Fallacy of Negative Premises. In these 
and some other cases the badness of the reasoning 
ought to be apparent to any one who has carefully 
studied what I have said about the syllogism. But an 
argument may seem to agree with the rules given and 
yet may be fallacious, owing to some confusion in the 
meaning of the terms or propositions. We must con- 
sider in what ways such fallacies are most likely to 
arise. 



XXVI.— FALLACIES OF AMBIGUITY. 

173 Perhaps the most common cause of bad reason- 
ing is the use of ambiguous terms, which mean 
one thing in one place and another thing elsewhere. 
A word with two distinct meanings is really 
two words. If a person were to argue that his ail- 
ment is a cold, and that all cold is dispelled" by heat, 
therefore his cold will be dispelled by heat, it would 
be absurd thus to confuse together a cold or catarrh 
with the absence of heat. To argue thus is as bad as 
having four terms in the same syllogism, and comes 



XXVI.] FALLACIES, I15 

in fact to the same thing. But in many cases it is by 
no means easy to see that we are using the same word 
with two meanings. 

174. It has recently been argued that since all men- 
dicants can be punished by law, and Sisters of Charity 
who ask for subscriptions are mendicants, therefore 
Sisters of Charity who ask for subscriptions can be 
punished. On the same grounds, however, anyone 
who goes about soliciting subscriptions for a charitable 
purpose, would be liable to be sent to gaol as a rogue 
and vagabond. A mendicant is no doubt one who 
begs ; but we must not convert this proposition simply, 
and say that whoever begs is a mendicant. A true 
mendicant not only begs, but Hves upon what he gets 
by begging, and does no useful work in return. When, 
therefore, the law punishes mendicancy, we must take 
care that it is applied only to those who beg for their 
own support, and make themselves a nuisance to the 
public. Lawsuits frequently arise from the difficulty 
of deciding exactly what words mean. A kind of dull 
black shaly rock has in late years become very valuable 
because it can be used to make petroleum. Some of 
this mineral, known as the Boghead coal, having been 
found in an estate in Scotland, a great lawsuit took 
place to decide whether it was or was not really coal. 
The uncertain meaning of a word may sometimes be the 
cause of war between great nations. The long dispute 
between the United States and England, about what was 
called the Alabama Case, turned on the meaning of the 
expression '' to equip a ship of war.'' International 
law allowed the building and seUing of ships of war, 
provided that they were not sent out fully equipped 
for fighting ; but there were differences of opinion as 
to what equipping meant. 

175. At the time of the French Revolution some 
philosophers argued that kings and rulers ought to do 
exactly what the people like, because they are the 



ii6 PRIMER OF LOGIC. [xxvi. 

*' servants of the people," and servants should obey 
their masters. But here is an obvious fallacy of am- 
biguity. Kings and rulers ought, no doubt, to serve 
their people, in the sense of doing what is on the whole 
most beneficial to the people. But there is little or no 
analogy between service in this sense, and the service 
of footmen, porters, and domestic servants generally 
who are paid to give aid to their employers when desired. 
People fall into a somewhat similar confusion of ideas 
when they think that, because a member of parHament 
is elected to represent a certain borough or county, 
therefore he is bound to vote according to the wish of 
the people who elected him. 

176. There are, indeed, several kinds of fallacy 
arising from ambiguity, which may be more or less 
exactly distinguished. Sometimes the confusion 
arises between a term in its collective and 
its general meaning, and I pointed out in Art. 17, 
the need of bearing in mind the existence of collective 
terms. It would be obviously absurd to argue that 
because all the books in the British Museum Library 
are sure to give information about King Alfred, there- 
fore any particular book will be sure to give it. By 
*^ all the books in the British Museum Library," we 
mean all taken together. There are many other cases 
where the confusion is not so evident, and where great 
numbers of people are unable to see the exact differ- 
ence. The absurd clamour about the Tichborne trial 
probably arose from people thinking that, because 
almost any witness brought against the claimant may 
be mistaken, therefore the whole of the witnesses taken 
together may be mistaken. Looking, again, to the 
things said and done by the claimant, it can be urged, 
that he may have forgotten the French language ; he 
may have forgotten the name of his mother ; he may 
have mistaken the number of his regiment ; he may 
have confused the name of his ship with that of another 



XXVI.] FALLACIES, 117 

ship ; and so on, through the hundreds of facts brought 
out at the trial. But though a man, under the circum- 
stances, might have done any of these things, it is 
exceedingly unlikely, and indeed quite incon- 
ceivable, that he should have done all of them 
together, had he been really Sir Roger Tichborne. 
It is the collecting together of a great many slight and 
independent facts, which sometimes makes circum- 
stantial evidence, as it is called, as complete a proof 
as can be needed. 

177. It may be shown that members of trades-unions 
often fall into a fallacy of the same kind. They argue 
that stone-masons, by limiting the number of appren- 
tices, may raise their own wages ; carpenters can do 
the like ; and also brickmakers, engineers, cotton- 
spinners, and so on through the whole hst of trades. 
It is quite true that any one trade may do so to 
a certain extent ; but it does not follow that all trades 
taken together can do it, because each trade, in thus 
raising its own wages, tends to injure the others in 
some degree. We may see in this and many other 
cases, that a logical distinction, which seemed absurdly 
obvious when first stated, may really be overlooked by 
immense numbers of men, and the confusion gives rise 
to very great harm. 

178. It is probably a fallacy of this kind, too, which 
leads persons to argue that a very rich man ought to 
give a handsome subscription to a particular institution, 
because he would never feel the loss. It may be quite 
true that he would never feel the one subscription 
sohcited, but exactly the same argument might be 
used in many other cases. The richest person would 
soon be ruined by the great number of demands which 
could be made on the same grounds. What a sub- 
scriber must look to is not the effect of each separate 
subscription, but of the whole of the subscriptions 
which may be expected from him. 



Ii8 PRIMER OF LOGIC. [xxvi. 

179. We sometimes fall into the opposite fallacy to 
that last described, and argue that, because something 
is true of the whole of a group of things, therefore it 
is true of any of those things. It is the fallacy of 
arguing from the collective to the general. 
All the soldiers in a regiment may be able to capture 
a town, but it is absurd to suppose that therefore every 
soldier in the regiment could capture the town single- 
handed. White sheep eat a great deal more than 
black sheep ; but that is because there are so many 
more of them. Ministers sitting in Cabinet Council 
will probably come to a wise decision concerning an 
important question ; but it does not follow that any 
one of them alone would come to a wise decision. 

180. Moral teachers are fond of encouraging us 
with various good proverbs, such as '' Labor omnia 
vincit." It is difficult to say exactly what is meant by 
" Labour overcomes all things/^ unless it be that a 
sufficient amount of labour will accomplish any 
practicable scheme. But of course it does not follow 
that, because a great collective amount of labour will 
build a pyramid, or make a canal, or compile a cyclo- 
paedia, therefore a single person's individual labour 
can do such tasks. The proverb has little or no value, 
because every person can give his own meaning to 
"all things." It is said again, that ^' what man has 
done, that man can do." As I am a man I might 
infer logically from these premises, that I can swim 
across the Channel Uke Captain Webb, or write a 
Paradise Lost like Milton, or discover a new way of 
making steel like Bessemer, or conquer an empire like 
Clive. The only way in which the proverb is really 
true is that, among a collection of a great many mil- 
lions of men, we can find those who can do all these 
things. Proverbs often seem very wise, because they 
are very ambiguous. 

181. Other fallacies arise, not from the confusion in 



XXVI.] FALLACIES. 119 



meaning of any one term, but from the uncertain 
meaning of a whole sentence. There is a hu- 
morous way of proving that a cat must have three 
tails : Because any cat has one tail more than no cat, 
and no cat has two tails, therefore any cat has three 
tails. As another instance of the way in which we can 
put nonsense into the form of an apparently good syl- 
logism, take the following : No kind of spirituous liquor 
ought to be drunk in excess ; but water is no kind of 
spirituous liquor : therefore water ought to be drunk 
in excess. It seems as if "" no kind of spirituous 
liquor" made a good middle term; but it is not so, 
and there are really two negative premises from which 
we can conclude nothing (Art. 81). 

182. A common kind of fallacy with orators and 
those who have to make the best of a bad case, is 
proving the wrong conclusion, and leaving 
people to imagine, in a confused sort of way, that the 
case is established. This was the device of the Irish- 
man, who was charged witTi theft on the evidence of 
three witnesses, who had seen him do it ; he proposed 
to call thirty witnesses who had not seen him do it. 
Equally logical was the defence of the man who was 
called a materialist, and who replied, " I am not a 
materialist ; I am a barber." The officious friend 
who gives advice is likely to be reminded of the 
proverb about preaching and practising. But even 
a drunkard may properly denounce the evils of 
tippling, and there is no direct connection between 
the logical strength of an argument and the characters 
of those who use it. 

183. One very dangerous kind of fallacy, not much 
noticed in books on logic, but of somewhat the same 
kind as the last named, is the fallacy of supposing 
that the failure of an argument tends to prove 
the opposite conclusion. Old Mr. Weller, as we 
all know, had the highest opinion of an " alibi 3 " but 



I20 PRIMER OF LOGIC. [xxvi. 

lawyers say that nothing turns a jury so much against 
a prisoner as the breakdown of an attempt to prove 
an alibi. WilHam Sykes being charged with burglary 
at Bow at one o'clock in the morning, brings witnesses 
to prove that he was in Whitechapel at that time ; but 
in cross-examination it turns out that, at the best, he is 
proved to have been at Whitechapel at midnight, so 
that he might have been at Bow by one o'clock. The 
jury are apt to assume that therefore he was not at 
Whitechapel at one o'clock, but at Bow. Yet, unless 
deduced from something in the character of the wit- 
nesses, or the obvious bad faith of the attempt, there 
is no logical force in the inference whatever. 

184. No number of failures in attempting 
to prove a proposition really disprove it. 
There is a general law of mechanics known under 
the name of the parallelogram of forces, which is 
undoubtedly true. A great many ingenious philo- 
sophers have puzzled their brains, and written books 
to prove it true, but none of them have succeeded, 
except by assuming some other almost exactly similar 
proposition to be true, which is begging the question 
Many well-meaning men have published illogical argu- 
ments to prove the existence of a God, and it is for- 
tunate that their failures have no logical effect upon the 
truth of that which they hoped to demonstrate. 

185. I mentioned in the last Article that several 
philosophers had tried to prove a law of mechanics, 
but had begged the question by assuming some almost 
exactly similar proposition to be true without proving 
it. This fallacy of begging the question con- 
sists in taking for granted that which has to 
be proved, and is of great importance, because the 
fallacy is very difficult to detect and explain, and 
occurs in several different ways. Sometimes it arises 
from giving a name to a thing, and then supposing 
that we have explained the thing. A wise man, as 



XXVI.] FALLACIES. 121 

well as a child, may reasonably ask, why can we 
see through a glass window ? Nobody has yet been 
able to give a reason why glass, crystal, and various 
solid things can be seen through, while most solid 
bodies cannot. But we sometimes hear it said that we 
can see through glass, '^because it is transparent." This 
is clearly begging the question ; to say a thing is trans- 
parent is neither more nor less than to say that you can 
see through it. The French dramatist Moliere ridiculed 
fallacies of this kind very cleverly. The father of a 
dumb girl wants to know why his daughter is dumb. 
" Nothing is more easy than to explain it ; " says the 
physician Ignarelle ; ^'it comes from her having lost 
the power of speech." ''Yes, yes," objects the father, 
" but the cause, if you please, why she has lost the 
power of speech." Ignarelle is quite ready with an 
answer. '' All our best authors will tell you that it is 
the impeding of the action of the tongue." 

J 86. The most frequent way, perhaps, in which we 
commit this kind of fallacy is to employ names which 
imply that we disapprove something, and then argue 
that because it is such and such, it must be condemned. 
When two sportsmen fall out in some matter relating 
to the subject of game, one will, in all probability, 
argue that the act of the other was unsportsmanlike, 
and therefore it should not have been done. Here is 
to all appearance a correct syllogism : — 

No unsportsmanlike act should be done ; 
John Robinson's act was unsportsmanlike \ 
Therefore, John Robinson's act should not have 
been done. 

This is quite correct in form ; but it is evidently 
the mere semblance of an argument. ''Unsports- 
manlike" means what a sportsman should not do. 
The point to be argued was whether the act fell 



122 PRIMER OF LOGIC. [xxvi. 

within the customary definition of what was unsports- 
manhke. 

187. People who do not Hke examinations are fond 
of saying that pupils are crammed for the purpose of 
passing them, and then they imply that the knowledge 
thus gained by " cram," is of little value. But this is 
very bad reasoning, and consists in falsely assuming that 
all or most candidates for examinations are crammed 
in the same way. If a pupil, being quite unable to 
understand a proposition in Euclid, learns it off by 
heart, and then writes it out in the examination room, 
as if he knew what he was writing, this is a bad case 
of cram, and the pupil gets no good beyond the 
exercise of memory. But if the pupil works up some 
books of EucHd, and can answer questions on them 
intelligently, he may have crammed them in the sense 
of doing it to pass the examination, but he has done 
it in a totally different way. Even though he forgets 
the problems in a few months or years, his mind will 
have been exercised in the best manner. 

188. Words like " Cram " and '' Unsportsmanlike," 
which are used in this fallacious way, have been called 
question-begging epithets, and we should always 
be on our guard against being misled by them. It is 
a good proverb which says " Give a dog a bad name 
and hang him." 



XXVII.— FALLACIES IN INDUCTIVE 
REASONING. 

189. I have already explained that the way in which 
people very commonly argue from one particular case 
to another is a very faulty and inaccurate mode of 
reasoning. It depends upon assuming that there exists 
some general resemblance or analogy between the 
cases, but in a great majority of instances people 



XXVII.] FALLACIES, 12.1 

make these inferences without taking the trouble to 
ascertain that there are sufficient grounds for what 
they do. People often disregard all precautions and 
assume that the medicine which suits one person will 
suit another, or that what cures one disease will cure 
another. There is in all persons at all ages a 
tendency to hasty and false generalization. 
The difficulty is not in making inferences, but in making 
correct ones. The mind is so framed that we cannot 
help classing together things which look like each other. 
The child does this as soon as it can speak a few 
words ; it calls other men " papa " as well as its own 
father, because it has no clear idea of resemblances 
and differences between them. A beaten dog fears a 
stick even m the hands of a person who would never 
think of using it upon the dog. But persons with 
reasoning powers vastly greater than those of the child 
or dog often use them quite as faultily, and generalize 
in a very rash and careless^ manner. 

190. Travellers sometimes make a rapid journey by 
railway through a foreign country, and then come 
home and write a book, as if they knew all about the 
country. They judge of miUions of people by the 
few that they get to know slightly in hotels or public 
conveyances. If they are cheated by one or two 
people, they infer that most of the nation are dishonest. 
Too frequently we judge savage or partially civilized 
people from unfavourable specimens, with w^hich alone 
travellers come in contact. The savages living on the 
shores of some unexplored lands, like New Guinea, 
have probably been ill-treated by the crews of trading 
vessels. Hence they are very unfriendly to strangers. 
But we ought not to generalize and infer, that all the 
inhabitants of a large country like New Guinea are 
exactly like those on the coast. Up to the present 
time, foreigners have not been able to travel safely 
in China, and can hardly visit more than Hong Kong, 



1 24 PRIMER OF LO GIC [xx v 1 1 , 

Shanghai, Canton, Hang Kow, and a few other ports. 
We ought not to suppose that the whole of the vast 
population of China is like that with which we are 
acquainted in these towns. 

191. There is really no good reasoning at all in 
assuming that other things or persons are like those 
which we have seen. In getting a sample of wine 
from a cask, as before explained (Art. 155), we know 
that it has been well mixed up, and, if requisite, we 
could mix it on purpose to make the sample a fair one. 
But we cannot mix up the population of a kingdom, 
and therefore we must not generalize about them un- 
less we have seen so many persons, in different places 
and ranks of society, as to render it very probable that 
we have got samples of all the principal kinds. We 
should especially beware of judging about any people 
or place from newspaper reports of what happens. 
As people are most interested in reading about strange 
and serious events, such as murders, robberies, great 
accidents, riots, absurd deeds, and so forth, we fre- 
quently hear about these things, but not about the 
innumerable peaceful and every-day events of life. 
During the last few years, the newspapers of Man- 
chester and Liverpool, have drawn attention to the 
savage way in which Lancashire men kick their wives 
and their friends, not to speak of unoffending strangers. 
Nevertheless, visitors from the more polished southern 
counties need not fear to meet a brutal kicker at every 
street corner. Fortunately, the kickers are still so 
small a proportion of the whole population, that we 
should hardly know of their existence but for the 
newspapers. Judging from the contents of American 
papers, especially as quoted in English papers, it might 
seem as if American gentlemen were constantly shoot- 
ing their intimate acquaintances in bar-rooms ; but, I 
suppose, a man may live in America all his life without 
seeing a revolver fired. 



XXVII.] FALLACIES, 125 

192. In this way trades-unions and societies of 
working men have been unfairly treated. Because 
some such societies have, at one time or another, em- 
ployed people to commit illegal acts to punish work- 
men who broke the rules of their union, it is false 
generalization to speak of all unions as if they did 
the same. We cannot suppose that all working men, 
or all societies of working men, are exactly like each 
other, and it is most unfair to judge them all by the 
few worst cases which happen to be made public. 

193. All the instances described in the last three 
articles are cases of false and hasty generalization. 
But we may without much difficulty distinguish three 
kinds of bad reasoning of the nature alluded to. 
Sometimes we argue wrongly that what is really true 
of a great many things, and, as a general rule, is also 
true of some special case which does not properly 
come under the rule. We extend the generalization 
too far. At other times we begin with that which is 
true only in certain special cases, and then treat it as 
if it were true of many things, and as a general rule. 
In the third place, we sometimes argue from one case 
which is peculiar, to another case which is also peculiar, 
so that there is no connection or real analogy what- 
ever. These three kinds of fallacies we may then 
describe as (i) from the general to the special ; 
(2) from the special to the general ; and (3) from 
the special to the special. 

194. It is a general law that all plants grow by ab- 
sorbing carbon from the air under the influence of 
sunshine. If, therefore, we shut up a plant in a cellar, 
where no daylight can reach it, we should find it would 
not grow, as a general rule. But we must not apply 
this general rule to certain special cases, as, for instance, 
where a plant derives nourishment from a bulb, or 
tuber ; potatoes, hyacinths, Jerusalem artichokes, and 
many like plants will sprout and partially grow in the 



126 PRIMER OF LOGIC. [xxvii 



dark. Toadstools, mushrooms, and other kinds of 
fungi, again, are so different in many respects from 
flowering plants, that we should hesitate in applying to 
them any rule that has only been learned from the 
observation of flowering plants. A fungus is, in 
fact, capable of growing upon the carbon contained 
in the soil, and without the aid of light. Great quan- 
tities of mushrooms eaten in Paris are grown in 
caves under the town, and that delicate kind of edible 
fungus called the truffle grows altogether under the soil. 

195. In legal matters we are frequently in danger 
of applying a law to cases which were not intended to 
come under it. Even when no special exceptions are 
mentioned in laws, bye- laws, or regulations, it may be 
evident that such exceptions exist. It is a very neces- 
sary regulation on railways that no one shall be allowed 
to jump out of a carriage in motion. But it is clearly 
understood tnat such a rule does not apply to railway 
guards, and other servants, who, by practice, can do 
it with much less risk than other people, and are often 
obliged to do it. Even a passenger would not be 
punished for breaking such a regulation, if he could 
show that there was more danger in remaining within 
the carriage than in jumping out, the only object of 
the rule being to save people from danger of injury. 

196. Nothing is more clear in the laws of England 
than that no Englishman can become a slave, and a 
well-known song asserts in the most positive way that 
'' Britons never shall be slaves.'' Yet the judges are 
continually occupied in sending persons into penal 
servitude, which is only a longer name for slavery. 
The fact, of course, is that the general rule about 
Britons is not intended to apply to the exceptional 
case of crnninal Britons, though we seldom think of 
this when repeating the popular words. 

197. The next kind of fallacy mentioned was that 
of ivrongly arguing from a special case to a 



XXVII. J FALLACIES. 127 

general law. If we were to infer that, because 
arsenic, and strychnine, and prussic acid produce 
death when taken in considerable doses, they always 
produce death, we should be mistaken, because they 
are frequently given as medicines in exceedingly small 
quantities and much diluted. A large number of tee- 
totallers want to prohibit the sale of spirituous liquors 
altogether, and the reason which is sometimes given is 
that alcohol is a poison. It is quite true that when a 
large quantity of strong alcoholic spirit like rum or 
whisky, is drunk, it may produce death like a strong 
poison, and if taken frequently in too large quantities 
it is very injurious. But it is a fallacy to argue that 
it is therefore " poisonous '' when taken in small 
quantities, and mixed with plenty of water. As I 
have already mentioned the most terrible poisons 
cease to be poisonous when taken in sufficiently small 
doses. It is all a question of degree and quantity. 

198. There only remains to be considered that third 
kind of false generalization, which consists in arguing 
from one special case to another special case, between 
which cases there is no real connection. It would be 
absurd to argue that because a man when assaulted is 
justified in knocking his assailant down in self-defence, 
if he can do it, therefore one prize-fighter is justified in 
knocking down another. Each is a special case, and 
there is no true analogy between them. The practice 
of betting is sometimes defended on the ground that 
people are not blamed for speculating in cotton or corn. 
Why, then, should not people speculate upon horse 
races? The fact, however, is that speculation is not to 
be approved unless it brings advantages to the public. 
Speculations in corn, cotton, and other goods do, on 
the whole, bring advantages, both to the public and 
to those who make the speculations with the hope of 
profit. But speculation upon horse races does not 
bring any such advantages, and far more injury is done 




PRIMER OP LOGIC. , [xxvu. 

to those who lose by betting than can be balanced b) 
the profits of those who win. 

199. It is not difficult to see that the fallacy here- 
described as arguing from one special case to another 
is only a kind of fallacy of false analogy (Art 167). 
But it is impossible too often to remind people that, 
on the one hand, all correct reasoning consists 
in substituting like things for like things, and 
inferring that what is true of one will be true of all 
which are similar to it in the points of resemblance 
concerned in the matter. All incorrect reason- 
ing, on the other hand, consists in putting one 
thing for another when there is not the requi- 
site likeness. It is the purpose of the rules of 
deductive and inductive logic to enable us to judge as 
far as possible when we are thus rightly or wrongly 
reasoning from some things to others. 



THE END. 



